I thought A major would be a good place to start given the end of the 2nd movement (which ended in A major). I feel it gives a smoother transition between movements. This being said the 1st movement is in Bb major, which is the nominal key of the quartet. As I think you point out, it doesn’t make too much sense to say the quartet is in Bb major given most of the quartet is in A major for a fair amount of time. (Although technically as the 1st movement is in Bb major it doesn’t matter what the other movements are - it’s perfectly allowed to say it’s in Bb major). Nevertheless it would probably have been a better artistic choice to have this movement end in Bb. Oh well - there is very large variety of quartets being composed these days (incorporating atonality, extended techniques, non-traditional sounds, forms, etc.), and I’d argue that the fact the key of this movement is A and not Bb is a fairly minor consideration. Any quartet who wants to play it is free to transpose everything up a semitone if they like 😂 Perhaps I should remove ‘in Bb major’ from the title and just call it ‘Quartet No. 5’. With regards to MuseScore - there are a few different types of trills you can add to a note, you can add the ‘tr’ symbol or one that looks like ‘tr~~~~~~~~~~~~’ which gives an extended trill for the duration of the note. The latter is what I used here which gives a much nicer, sustained trill. Also note that MuseScore is not so good with flattened/sharpened trills (ie a trill with the higher note a semi tone higher or lower than otherwise indicated by the key signature) , it doesn’t like them and I can’t figure out a way to make it play them except to change the key signature in MuseScore momentarily, for the purposes of playback only.

But anyway thanks 😊