I looked over the arrangement. Yes, the issues Thomas laid out are important. Mostly that means you have to figure out what bells are appropriate for your 3 octave choir.
Beyond that... I looked at the Garee score (I haven't seen the Thompson score). Rhythmically the lower treble (well, the whole piece) is very much level 2. Most of the time these battery ringers have no techniques to worry about.
So the difficulty is, as you mention, only in handling the accidentals.
Which leads to a question -- what do you propose to do instead? Simplifying the harmony would significantly change the character of the piece, so not really possible. Changing the key, transposing the piece up or down only moves the bell change problems from one person to another. Transposing also makes the range issues that Thomas mentioned more of a problem. And transposing (or any other simplification) means copyright issues.
So I see two options:
1. Don't play the piece. Some pieces just aren't a good fit for some choirs.
2. Do careful analysis of the problem spots. Have the ringers practiced switching bells? Do they know how to weave? Do they know how to mark music to put down a bell when it is last used before the accidental and when going back to the regular note? If a spot still looks complicated can they sweet-talk a neighbor into helping them out?
Bell changes have been a part of our music ever since we wrote in accidentals. A bell ringer should know how to handle them. If you need help, that's what we're here for.
Paul Kinney
Redford Aldersgate, UMC
Redford, Michigan