I really don't think the differences are big enough for me to be very concerned, but yes, watching a stage version is a very good idea!

If someone offers the musical and prefers it to the film, it may feel to them as though you're asking for a different version of canon than the one they have agreed to write for your request.

I made sure to state in my letter that if there were differences, the author can choose whichever they prefer. They shouldn't have to match it to my mistake.