I would like to create a schola of male voices, singing at just one or two Masses per month. (The adult choir sings once each weekend September thru May and rehearses each week during that time.) The schola could rehearse immediately after the adult choir, however, I am wondering if I should keep the two completely separate. Is there any wisdom in creating the schola to be by invitation only?

I would indeed like them to eventually be able to sing both the ordinary (in Latin) and the propers in English.

We had success implementing a chant schola about 10 years ago in a similar situation (except it was EF instead of OF). Some members of the choir - of which we are all singing - approached me about forming a schola. At that time, the choir sang few (if any) chant ordinaries and only the Rossini propers.

I went to the director of the choir and asked if we could form a sub-group of the choir and, several times a year, sing the full propers rather than the Rossini. She very graciously agreed, and she and I determined a schedule of Masses at which the schola would sing the propers - we only chose four Masses that first year to see if it would be something that would "stick".

Went back to the men, and suggested rehearsal that would either be an hour before or after the regular choir rehearsal. That first year, we only rehearsed 3-4 x before the given Mass for which we sang the full propers (Christmas Day, Easter, Corpus Christi, and Pentecost).

At the end of the year, the men had made lots of progress and asked about continuing. I went back to the director who said - sure, as long as I can join the schola! She and I worked out a more expanded schedule of 12 Masses the following year, and we jumped from 5 men to 11 mixed voices (including some new members who joined the choir).

Eventually, the schola was no longer a sub-group of the choir, but became its own entity. We sang at Masses around the diocese, and started acquiring members from other parishes as well. In that second year we added the full Holy Week Triduum and about 14 Masses at another parish along with vespers (about 10-12 x that year). We began learning more advanced polyphony as well as chant including ordinaries.

People from the original parish tended to be part of both groups, although our rehearsal shifted to be nearly equivalent - 60 minutes for each group if I remember correctly. The members of the schola from other parishes would show for the schola practice and then leave when the choir practice started - but our parish choir was still the full group.

It turned out to be something that not only elevated the knowledge of chant; it became a way of introducing high-caliber polyphony (the choir members that gravitated to the schola tended to be the better singers in the group); more importantly, it exploded the opportunities for different types of Liturgy in the parish dynamic. Tenebrae, regular weekly vespers, occasional Christmas Matins, lots more feast days...

Just some thoughts!

Check out "How to Start Your Own Garage Schola" by Arlene Oost-Zinner here:

https://www.catholicculture.org/culture/library/view.cfm?recnum=7378

Anyone have an opinion on whether to introduce chant notation from day one or stick with modern notation while getting started?

Chant notation from day one.

I know it sounds silly - but my experience has been that is more difficult to convey nuance of interpretation via modern notation, in part because it reinforces the (incorrect from my perspective) concept that all notes are equal in duration. There is a constant ebb and flow of tempo and dynamic, and I find the chant phrasing is easier to explain within the chant notation.

I think it is easier to "think" chant via chant notation - and "think" polyphony via modern notation...

Your question arises from a putative understanding of chant (a thing that is sung) and chant notation (instructions on how to sing it) as not being a unity, two sides of the same coin; and that another, conceptually and fundamentally different notation which does not give guidance as to how to sing it, giving naught but pitches, might do just as well. This, as I'm sure you will agree, is not so. Chant and chant notation are a unity. Only those who fail to understand that unity could entertain borrowing another notation (impossibly) to fulfill the role of of chant's native notation.

The misapprehension that a non-chant notation will do just as well as chant notation is an error found even in most academic and scholarly works on chant. As if a row of note heads and slurs could communicate the nuance and niceties of performance as 'square notes'. It is sad that scholars of high repute think of chant as a sequence of notes, pitches. Throw your scholars 'in the water' and watch them swim!

Re. notation: FWIW: I can sight-read melismatic Offertory verses without any difficulty in chant notation, but will continually trip over something as simple as the "Gaudeamus" Introit if rendered in modern notation. (And not because I'm not proficient in modern notation, I am--it just doesn't work for chant.)

..from the American Gradusl...

I read somewhere last year that Bruce Ford was putting his American Gradual into chant notation. I've not heard about the status of that endeavour, but I do hope that we'll see that it actually happens.

Mad makes some salient points worthy of consideration.
I would add though, that...

I believe that the most confusing aspect of chant notation, other than acquiring 'modal ears', is the movable clefs and the difficulty acquiring proficiency as to where the half and whole tones belong. As for square notes in and of themselves, I cannot believe that anyone of normal intelligence should have difficulty reading them. Some people just throw up their hands at anything that may require a bit of learning or thinking, and they will throw up all manner of facetious whining to rid themselves (and deprive everyone else) of it. I have no pity for those who whine and whine, and insist that they 'can't' read chant notation. I've had many people over the years tell me that square notes were easier than modern notation

It is possible to devise a system using round (or triangular or trapeziodal) notes rather than square, (as if the shape of the notes were the real problem - it isn't), but it has yet to be done. I am reading several treatises on various aspects of the offertory in history. These essays, by the finest and most learned university scholars of our time, give their examples in rows of round noteheads and slurs, oblivious (apparently) to the fact that their examples don't begin to indicate how actually to perform the chants which they illustrate, examples going back as far as the pre-Carolingian age. This is poor scholarship. These same scholars would do well to study Cardine's Gregorian Semiology, study the symbiotic relationship between Carolingian and square notation, and to cultivate an interest in how to perform chant as well as analyse it structurally and compare the various chant dialects melodically.

It is possible to devise a system using round (or triangular or trapeziodal) notes rather than square, (as if the shape of the notes were the real problem - it isn't), but it has yet to be done.

What about "shape notes" ... in particular, the 4-shape note system? The four shapes are represented also by syllables, borrowed from the Guidonian solmization. "Fa" is a triangle (the upper right half of a square cut by a diagonal), "Sol" is an oval (same as a modern "round" note), "La" is a square shape, and "Mi" is a diamond shape.

Mode I (with flatted Te) would be rendered with the shapes: La, Mi, Fa, Sol, La, Fa, Sol, La (in solfege: Re, Mi, Fa, Sol, La, Te, Do, Re). It's the same as the modern natural Minor scale. Mode I with natural Ti would be rendered with the shapes: Sol, La, Fa, Sol, La, Mi, Fa, Sol.

Shape notes appeared in the U.S. in publications towards the end of the 18th century, in particular, in music written by William Billings (and engraved & published by Paul Revere).

There is also a 7-shape system with shapes corresponding and named by the traditional solfege syllagles.

Chant is sung text, and grouping the notes according to the syllables of the text is an important aid to rendition, particularly for singers who are not professionals. The even spacing of the note heads is a hindrance, although substantially mitigated by the beams.
Of course many of the nuances are not in the (semi)official editions, the nuances shown by Hakkennes here on the second page are missing from those editions, and Hakkennes seems closer to what our organist plays.

At the very beginning, my chant teacher introduced the first antiphons without any partitions, just by ear and memory. I found that very useful, because it helped memorize lots of patterns that you find then in lots of other places, and it helped with keeping in mind that we were not singing notes, but words and text.

the difficulty acquiring proficiency as to where the half and whole tones belong.

For a string player this is easy in one's accustomed notation; keyboardists may not have this advantage. Being a cellist/gambist fluent in C clefs I just had to cope with 4-line staves to start chanting, but other instrumentalists might not have that head start.
I've seen vast amounts of rehearsal time wasted by an otherwise reputable conductor who thought it impossible that the different shapes of a climacus could be sung at the same speed: a case where round notation would have been a decided advantage.