I seriously doubt there is anything going on that a new set of belts will not solve (replace both at same service).
Is this the first time you have considered changing the belts?
Or have the belts been changed previously?
If the belts have 200 hours on them, they have survived longer than I would have expected, especially with your description of hilly operation.
Likely what is happening is just belt slippage that is exaggerating the normal "free rotation" or "slack" in all the various places inside the transmission gear train.
ALL gear reduction power trains exhibit the characteristic of having some loose motion when the gears are rotated against each other. Where you have many meshing points in a transmission, the effect of this "backlash" at each point where gears mesh together is "additive", meaning that at little here and a little there all add up to a lot of looseness in the sum/total.
Normally, this sum of backlash causes no strange sensations or actions because the load being transmitted through the gear train is in a single direction. This keeps all the gears in contact with each other under constant pressure on just one specific face of all the gear teeth (cogs).
The point of contact will not change so long as the load is kept constant and evenly applied, as is the case when everything is in good order with drive components (belts etc.).
But what is probably happening in your circumstance is that going downhill, the weight of the tractor and gravity conspire to REVERSE the roles of the engine and transmission as to who is driving who.
Uphill, there is no question that the engine is driving the transmission, and the load is kept constant on one face of each gear.
But, going downhill, the transmission is trying to drive the engine, and this, plus worn belts, will cause the engine and transmission to alternate the roles of "drive vs. driven", and that will cause the loading of the gears inside the tranny to constantly switch back and forth from one face of EACH gear to the opposite face, and this is where you are picking up the noise and sensation that a lot of "thrashing" is going on, because it is.
Short of opening the transmission to inspect things, trying a new set of belts is the only sure fire way to get an answer.
You can demonstrate to yourself just how much total backlash is in the gear train by putting the transmission in gear with the engine off, parking brake released (not applied) and turning the big belt pulley on the transmission input shaft back and forth. The amount degrees of rotation you can move the pulley before you feel the tractor try to move on the ground represents the total backlash in the entire gear train. You will probably be surprised at how much there is.

Thanks mownie,
I'll order some new belts & give that a shot.
I'll get back in a week or so & let you know how it worked out.

What's happening is the belt has an idler it uses as a clutch. When the engine is putting power to the tranny the power is put to the side of the belt opposite the idler. When going downhill the power to the belt is reversed going thru the side of the belt the idler is on and since the idler has a spring in the linkage to maintain tension the "power" going thru that side of the belt tends to remove the spring tension from the belt making it looser.
I experienced this today while mowing at a friend's place and he has a steep road to get to his lower yard.
Mike

Well, I installed new drive belts...
I was feeling pretty manly after fishing the motor to the variator belt through the passage & on the correct side of all the keepers.
Unfortunately that didn't fix the runaway problem.
New belts did make a big difference in the response of the drive pedal.
But as soon as I turn down hill, gravity takes over & I hear a metal shop behind me.
Pretty sure If I opened the trans, I'd find a lot of metal chips & chunks in the grease.

I think I'll be done trying to repair it now.
I'll try to get a little more use out of it on the flat spots & rely on the other mower on the hills.
It was worth a shot.
Pity,
the motor feels like it;'s got a lot of life in it.

which belt would be the culprit ?

I don't know if Lowes still has the special on John Deere lawn tractors, $250 off normal price, but it would sure fix your problem if they do. It fixed mine, which is to be delivered in a couple of weeks.

MTD will tell you to replace both belts at once. If a front belt appears good, than it probably is and you are OK with installing just the rear as it wears much faster than the front. BUT, if you have the runaway issue, that is internal of the transmission.