Well have a good think about it
You have 2 independent drives each with it's own pump & motor units
You have 1 engine that powers both of them via the drive belt
If one drive was not working properly then one side would drive stronger than the other causing the mower to turn in an arc
If it is going strait then what ever is the problem has to be with the drive belt or engine
So either your engine is running below the 3600rpm it should be running at or the belt is slipping under load or the engine drive pulley is slipping on the PTO shaft
Now most MTDs have an inbuilt key in the pulley so we could ( hope ) the pulley is turning at full engine speed, bit it would not hurt when replacing the belt to pull the clutch & pulley off and check the key & keyway
So the drive system is a belt + a tension pulley + the 3 belt pulleys
When the tension is low the right side will work better than the left in both directions because the right side gets pulled by the drive pulley and all of the slack is between the left pulley & the engine pulley.
So the right works a lot better than the left , again causing the ZTR to travel in an arc .
Otherwise both of the drive units will need to have failed the same way at the same time which is highly unlikely .
Or both of the lap bars would have needed to go out of adjustment the same amount at the same time also unlikely .
The other thing that pops into mind is a lower speed towing setting
Some mowers like Toro TimeCutters have a slow / fast or tow / mow switch .
I have no idea if your Cub has one of these switches as I have never worked on one & don't have access to owners manual for it .
This is all I can offer
The new belt will be cheaper than the 120 mile round trip & even if the belt is not the problem, you will need a new on at some point in time so you wrap it in cling wrap and pop it in your shed for use latter on so it is not money down the toilet .