Thank you everyone for your help! I think I have solved the problem by winding the thread a second time around the little button at the beginning of the thread path for the top thread. Now instead of going around the button partway, the thread goes around a complete turn and partway. Cari-in Oly suggested that, and it seems to have worked. Yay!
I don't know if my machine has a screw in the top of the bobbin tensioner or not. Going to have to check for that for future reference.