We nearly always alternate solos on the Graduale, Alleluia and Offertory, just to give half of us time to rest a bit, since we are a very small schola (4 people). We don't always sing the Offertory verse, but if we do, the women usually do the solo on the verse. For the Graduale and Alleluia, the men take the one with lower overall pitch, and the women solo on the other. I have also, on rare occasions, sung an entire Mass alone (EF and OF). It's a lot of work, and it was always in a small chapel or in a semi-private setting or on a weekday when it wasn't feasible to get anyone else to show up. I also insisted on singing a the Graduale, Alleluia and Offertory alone a few times when I was with a substitute group that wasn't capable of singing those, as they are always more complex than the rest of the chants.

At some other churches I've been to (EF) there's a man who sings all the propers solo, and a mixed choir sings hymns and the ordinary (along with the congregation).

Those rubrics are, by the way, the ones found in the 1962 Liber.

Actually... no. The link you provided is a summary of rubrics and guidelines made by someone at St. John Cantius and posted on their site. But not everything in that summary is a rubric, properly speaking. Some of it is interpretative - i.e. "here's a way to do X".

EF Rubrics - properly speaking - for the Mass are found in the Missale, not the Liber. The Liber (strictly speaking) is not one of the seven Liturgical books. It does have a section of "Rubrics" (culled from other sources), but it doesn't talk at all about how to divide the choir or what cantors sing vs. what the choir sings... in most cases (there are a few exceptions) that is left to local custom and the resources of an individual parish.

The guidelines provided in the Liber for Advent I for the Gradual / Alleluia are not a "rubric". They simply demonstrate a division that can be (and is perhaps even commonly) used. But there are a variety of ways in which the division can be made. I've never sung in a choir (for example) where the cantors only re-intone the Alleluia after the verse (although I'm sure there are some who do). As I think you've seen from your other post, some choirs sing the Kyrie / Gloria straight through (full choir); others alternate. Some alternate men vs. women. Others alternate choir vs. congregation. For the Gradual / Alleluia, some parishes split that between men on one and women on the other; some sing full choir - perhaps with cantors on the verse, perhaps not; some have a small group (a sub-group of the choir) sing all or part; some have cantors-only that sing the entire piece.

Here is the section on Rubrics from the 1961 Liber (1962 is the same).