Wind bands are extremely widespread and are often happy to play new compositions, even if just once at a rehearsal. I've played student compositions myself while in my uni wind band, and I've had a composition played by them. However, this isn't quite a wind band piece - for example, the standard wind band orchestration includes 2 flute parts, 3 clarinet parts, 2 alto sax parts, 3 trumpet parts, and so on. It's flexible, but having 1 of each part makes it seem like it's for a very specific ensemble.
Yes, the timpani part is unplayable as is, because most of the time only 1 timpani is able to go down to that range of E and below, and you've written 3 notes in that range. Putting it up an octave would help, but it's also rare to get the top timp going up to a C.