Hi Fredrick!
Not being able to see your linkage, my guesses here will be little more than conjecture and experience, so if you can snap and post a digital picture of the linkage, any of us could verify, but:
Based on your description, it SOUNDS like the short link going from the brake-pedal bellcrank to the neutraling-cam-plate is either broken, or missing some parts... or some other component has come loose.
The first half of your description (slowing down) sounds like one of the ratio-control links had become un-lock-nutted, and was vibrating out. Then 'handle stuck' sounds like it had fallen out and jammed against something... and 'moving freely now but not controlling tractor' sounds like it's dangling, and the other end has fallen into the grass, or onto the deck somewhere.
All this being said, rest assured that you DON'T have serious problems... the hydrostat is most likely just fine, as is the transaxle... they're essentially bulletproof (literally, for anything smaller than a good rifle-round), and you've not had anything happen that put it in any self-destructive condition. It's simply a matter of correcting the linkage, and returning to the joys of cubbing.
Anybody got a digital picture of a 125 or similar linkage they can post for Fred? I don't have one here at the hotel... but I'll bet if he SAW one that was right, he'd KNOW what was missin' and Messin!
DK