I received the NOS cart, and its performance around the track was similar to one of my original carts, so the entry/exit cycle to the shed for both those carts is perfect. The feet on the new cart are relatively soft, but a bit firmer than the original carts, so I ordered replacement pads. I'll post an update on this thread after I test them out.
I said I thought 3 carts would work, but it didn't work so well in my initial attempt. After I moved on from that I found that my release mechanism (which I had greased at the start) was still sticking a bit. That may have been why the 3 cart cycling didn't work. I'll check that out and post an update on that with the above info.