I've also been trying to figure out how to do this on the cheap.
I think I had a last-resort epiphany last night, if I can't figure out how to use acrylic and need to end up using glass.
Thrift stores always have huge ugly framed pictures for pretty cheap (less than $1 if you go on sale days). I figure that I can just buy five huge super ugly picture frames and then take out the glass fronts in the frames and use them to make a display case.
I think this would work better for someone who isn't planning on taking off the cover very often, since the glass will probably be heavy and more prone to accidents? I'm still on the hunt for a cheap acrylic supply, since I'll probably want to be taking off the cover every other day or so...