Always Buy the Complete Toilet Repair Kit
When planning to repair a toilet, purchase a complete repair kit, and not just the part you think is broken. Otherwise you will just break the part you didn't buy.
So two trips to Home Depot later, the main level toilet works and even fills up quickly again. I believe the slow filling problem was caused by a rubber washer in the supply line; the directions explicitly state not to use a rubber washer if it's a plastic line, which it was. I guess the plumber we paid to fix it a few years ago didn't read the directions.
All this home improvement I've been doing must be going to my head, because today I bought a table saw.