Thanks for all the suggestions! The solution ended up being simpler than I thought. The Marine range where I shoot has a Meprolight Universal Sight Installation Tool that they let me borrow:
I don't think I'd drop the $500 it costs to buy one for myself just for occasional use, but it sure was nice; just had to choose the right position on the block to get the slide at the correct height, then spin the handle until the sights were where I wanted them.