In my location 97w has much better signal strenght. 125w especially Montana PBS is much weaker. I would use the 36" for 125w and the old dish on 97w.
The other option is a motor with the 36".
Totally agree with Jorgek, the 20'' dish is too small for 125 W. Here in CT I have a 31'' Ku dish and 125 W is tough to pull in, very intermittent signal for me on the weak transponders when the weather is bad. You're in NY, so you're pretty close to me, with a 20'' dish I'd think you'd have a hard time receiving 125 W Ku at all but the 36'' would probably pull it in ok. Even on 97 W you might have a bit of trouble with the 20'' and not receive all transponders.