I tried the soldering home made rings but decided to go with the ring terminals instead. The soldered rings weren't any thinner even when I tried to smash them flatter. I tried squeezing them flat with pliers and also tried a hammer. When I really smacked them with a hammer it could push them out of shape and make it harder to fit them on the terminal post but they still weren't thinner.
Re-wiring the lamp with 18 gauge was a help and I felt the end result was better with the thinner wire.