I got the brakes working. Problem was the nut between the steering wheel and the seat.
On this particular mower, what I was looking at in the "brakes engaged" state, was actually the brakes engaged. The spring isn't supposed to stretch any. I set the brake bar nut tension correctly and the very tiny amount of movement it had was able to engage the brakes. I can't explain why or how, but everything is working like it should again. Thanks, everyone, for the help.
They really don't make things like they used to.