I just (yesterday) had the exact same issue.
I have a Troy Bilt Bronco from 2004-2005.
MY Issues was a new belt I put on. The store when I bought the mower didn't stock the OEM belts any more... but I was "assured" the belt I bought would work fine.
They did check and it was the exact same length.
So I put it on and when I put it in forward (or reverse) away it went without me even pressing the gas pedal.
I took the "new" belt off and put on one that was OEM and that fixed the problem
Seems some of the newer belts are a bit 'wider' and so the belt grips the pulley faster.
I noticed when the tractor went forward... MAN it would FLY. SO it was "over gripping" (if that makes sense) on the pulley and the only way it was still was if it was in Neutral.