it is possible to adjust the temperament of any synth to match just intonation or any other temperament scheme - it is part of the midi spec and where an instrument was made before this part was added to the spec, you could do it simply by using system exclusive messages - if that doesn't get you there then careful experimentation and notation of pitch bend positions will allow you to adjust each note to the desired frequency in your chosen temperament.
your trombonist will have no difficulty adjusting to the new temperament as only the 1st position notes are fixed in tube length - everything else is adjustable by moving the slide further out or closer in. Even the fixed positions can be lipped up or down in pitch - I play trombone and this is a common enough technique to simply play in tune in equal temperament that adapting to another temperament is not a big deal - adjusting the ears (i.e. being aware of the new tuning scheme and matching pitch to it) will be. Your singer will likewise not have too much difficulty beyond learning the new tuning scheme.
The statements you make about ancient cultures tuning systems cannot be supported by facts, only by supposition mainly from those who want these ideas to be true.
What you say about adjusting temperament on keyboard it's interesting.
About the ancient cultures there are reseaches on ancient instruments to proove they where tuned in 432 as Richard Huisken says.
About the difference between even different keys I agree with produce dept the feeling changes.