Wow yeah that sounds really similar. I tried rocking the switch back and forth while starting and got nothing. There are several things that lead me to believe this is not a safety switch.
1) the battery light does not come on when I turn the key to the first position. I had in the past had my foot sitting on the treadle when trying to start and they battery light was still on. Same with the PTO lever being bumped, the battery light still came on.
2) I removed each of the safety switches and tested them with the ohm meter. In the open and closed position they read continuity or not as they should.
3) When I removed the OPC the fuel pump safety switch would not click but it does when it is on the tractor and the key is turned to the first position.
For you (as if I know what I am taking about) I would first try to jumper that treadle safety switch. It sure sounds funny that it may or may not crank depending on position.
If you take the dash off it is easy to find the 12v wire that runs in series from all of the safety switches. It is red with a black stripe and can be found at the back of the OPC. Or you can check it at each of the switches. It's easier to check it at the back of the OPC because if it is 12v all switches are satisfied.
Lastly it may help to get your hands on the WSM manual for your
b2920. I found a pdf version for my tractor on the web and found a european version. It's not the right year and some things are different but for the most part it explains everything in detail right down to pictures and wire colors and diagrams.
Is your battery light coming on at the console with the key in the first position?
Hey I don't want to revel in your misfortune but it's nice to know there is somebody else swimming in the rio de caca as Saul Goodman would say.
Cheers