Sorry, this is a day late and a dollar short, but maybe it could be useful for next year... One of my favorites for a postlude is Gerald Near's setting of Ave colenda Trinitas. We sang the chant and then I played the postlude. Near wrote another on "Adesto Sancta Trinitas" which is excellent as a prelude. (He has several small volumes of good organ music out and all the pieces are based on chant. Some have a 'jazzy' sound that I don't like quite as well, but most are really lovely.) There are quite a few small organ settings of "O lux beata Trinitas" by late Renaissance/early Baroque composers. One of my favorites is a stunning setting in the Dover edition of Sweelinck (but sometimes attributed to Scheidemann). It has two variations - you could use one for prelude and one for postlude. This year I played Flor Peeters's setting of "Grosser Gott" (Holy God, we praise thy name) after mass. It sounds like a short toccata but is 'monumental' enough for an important feast day. It has the melody in the pedal, which everyone should be able to recognize.

You could even play a motet for the feast on the organ - I do this frequently and try to use a different registration on each manual in order to get the polyphony to come out, doubling up the soprano and alto on the right hand, playing the tenor with the left on another manual, and of course the pedal for the bass. You can make whichever is the melody stand out more. Once in a while there's a melody in the alto, which tends to make problems for fingering etc. Then I use a 4' on the pedal for that, play the soprano with the right hand, and do tenor and bass with the left. I find that keeping a very strict tempo and making sure the cantus firmus can be clearly heard makes this early organ music come alive. If you play it all together on one soft registration with a huge 16' in the pedal it tends to die on the vine. It has to be sharply articulated and then it really jumps up and says something.

Then there are what I think of as the "abstract" pieces which are not based on a particular melody. The Bach preludes and fugues are great for solemn feasts, and there are a ton of others, which I'm sure you don't need anybody to tell you about.

The three kyries from Clavier-Ubung would be splendid.
One could do them all for a thrilling prelude,
or the first=prelude, the second=offertory or communion, and the third=postlude

There are quite a few English Tudor organ voluntaries on O Lux Beata Trinitas