Historically, these would most often have been played on one manual (or possibly alternating manuals), with a fair bit of ornamentation (used, it has been argued, as a dynamic device). Italian organs were flute-rich. The Ett is early-19th c. so you can do that with practically any stop combination that sounds good. Most important thing will be to make sure your chosen stops have enough definition down low, so that the bass can be heard clearly.

Go for it!

What a brilliant (and labour intensive!) idea.

There is certainly historical precedent for this, so you are on terra firma. I can't vouch for the continent, but there is an appreciable number of English renaissance and early baroque examples of motets transcribed as organ pieces or voluntaries.

As for registration, I would agree with Francis' suggestion - an 8' principal or flute, though I would probably use 8' and 4', maybe an 8' flute with a 4' principal. (A lone 8' flute is not likely to reveal the counterpoint clearly.) You can judge what sounds on your instrument bring out all the voices of the pieces in equal fashion. Strive for a 'clean' sound and avoid anything that sounds 'muddy'. Do not separate any voice on a solo stop, and do not use 16' sound in the pedal. In fact, if you use the pedal at all it should have no independent stops, but simply be the sound on your keyboard coupled to the pedal. No pedal at all would be desirable. You want to replicate the SATB vocal style of your originals and use a registration by which the counterpoint and interplay of voices is made clear.
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By the way - there is nothing like copying in one's own hand any literature that one is playing as a means of really learning and knowing what one is playing - especially for recital preparations! This is an excellent idea for students and professionals alike. (If it was good enough for Bach it's good enough for us!)