I'll try to answer this. I'm not familiar with S Scale . But have done numerous 3RS conversions.
I'm guessing your using an S Scale Kadee for this. From your post. It sounds like you only did one car. You pretty much can't run a passenger car with body mounted couplers mixed in with truck mounted couplers and not have a derailment. At least scale length ones.
Not familiar with a 20 inch curve. They seem a little tight. Even if you body mounted all your cars. 3RS you need at least an 072 curve. Preferably with easements to run Scale length passenger cars. Not really sure what a 961 passenger car is. I looked them up. They appear to be close to scale length cars.
I have no experience in S as far as Kadee's. Have done numerous 3RS conversions. Asumming youare doing this for one or two reasons. Either couplers on the cars are not reliable as far as staying coupled. Or you desire more of a scale look. If it's just a reliability thing. Can you use O Scale Kadee's. A little bigger. But more options. They offer a long shank coupler that will give you a lot more swing.