That was interesting. I pulled down my 78 parts box and the old switch was right on top (meant to be!). I hooked up some leads so that I could easily turn the key and listen to my meter-beeper (I know CO doesn't like them but mine has a readout to watch also) and found that R had continuity with B right away and to the end of rotation, but S was iffy and seemed to only have one narrow range where it had continuity. Then I remembered that I had pulled it apart in the past when I had a problem with my 76, and had ended up bending the internal actuating rod to make it work right.
Testing with the switch pulled apart and turning the electrical portion with a screwdriver showed that both S and R could be over-rated to where they lost continuity. The only thing controlling the total degrees of rotation is the mechanical (key) part of the switch So I'd guess that your new switch is just adjusted to turn the electrical switch too far. Not good news but it can be fixed, if you unstake it and take it apart. You can twist the flat rod with a pair of pliers. But I don't think it's right, it's a flaw in operation.
One big "Ah Haa" from back when I used to start the 78 parts car is that now I know why it would start to turn over then let go all of a sudden, leaving the starter spinning loudly. I thought it was a starter problem but now realize that it was just the ignition switch rotating past the contact and losing the S circuit. I spent a lot of time trying to reason that problem out and never really had a good theory.
Edit - more interesting stuff. I noticed that the brass male S pin was wobbly on the back of the switch. So I restaked it with a drift pin, put the whole assembly back together, and both S and R worked as expected, full continuity over the full Start rotation. So, check the pins on the back, maybe R is loose and can be reset with a little tap of a hammer.