With the game set for a 1-player game, and after it resets to start at Player 1, Ball 1, if you then manually step the Player Unit (by pushing in the step plunger) four times, does it then correctly advance to Player 1, Ball 2? And then so on, to Ball 3 and then to Game Over? This first test is to ensure that there's not a mechanical alignment problem with the wiper disc.

However, there's enough difference between the Snow Derby and Snow Queen schematic logic on the "Add Player Unit" path that I'd next recommend getting the schematic for Snow Queen. Otherwise debugging a logic issue with any precision will be more guesswork. Pinball Resource has the schematic available (pbresource.com). Can also pick up other basic items (ring kit, switch adjustment tool, flexstone, playfield cleaner, etc.). Takes a bit more time up front to gather these things, but will save a lot of time in the long run.

Otherwise, for a 1-player game, the Player Unit should pulse four times to go from Player 1 Ball 1 to Player 1 Ball 2. If it's not doing that consistently, and there's not a wiper disc alignment issue, then there are possibly dirty and/or mis-aligned switches. Every switch in the path to the "Add Player Unit" needs to cleaned/checked/adjusted, and that's where having the schematic for Snow Queen is needed (as Snow Derby is different).

The stopping and showing two players at once suggests the wiper disc may not be adjusted, so that's a starting point.

Shortening the spring and adding lube and such before doing a disassemble, degrease, and clean, is just masking issues. These old EMs really need to be methodically gone through one part at a time and rebuilt to achieve optimal results. Need to get as much of the old gunk off first, then see how it behaves.