I just fixed an issue that sounds very similar to this. Is the 1 to 10 bonus stepper (on the right side of the playfield, looks like a small score reel with no numbers on the reel) stepping while it's "stuck"?

The steppers on the underside of the playfield are:
1. Eject advance unit - left side about half way towards the head. Looks like a score reel without numbers.
2. 1 to 10 bonus unit - right side about half way towards the head. Looks very similar to eject advance unit
3. Strike bonus unit - right side, back corner (near the head). It's a big rectangular piece of Bakelite with a circle of river connectors on it (the picture in the manual is pretty accurate).

As the 1 to 10 bonus relay turns, watch the plastic switch activator. When it's at zero, it should be down. If I recall correctly, the bottom switch is open at zero and the top is closed. When it's in any other position, the actuator moves up, the closed switch opens and the opened switch closes. On mine, the last position before zero makes the actuator go up even more (doesn't change switches, but don't be surprised to see that movement). Then going back to zero it goes down again to return switches to original positions. You can manually pull and release the solenoid to watch this happen and see if switches open and close properly. Once you know what it's supposed to do, watch the reset cycle and see if it's ending at zero position. (I had a switch not opening far enough so current was arcing across the gap when it was supposed to be open.) Also watch to see if the solenoid is is going through full range of motion when pulled in and released.

The strike bonus unit is a step up, step down stepper. When a strike is scored, it steps up *twice*. When bonus is counted, it scores 5 times per position (10 times per strike) until reaching zero. If the game was turned off when it was at game over state, it would already be at zero, so it would not need to reset. You can try manually stepping up and stepping down. Try a reset cycle when it is at a non-zero position to see that it steps down. (Once I realized what happens here, it made much more sense why a reset takes much longer if the game was powered off mid-game with some strikes scored.

I can't check mine right away, but I suspect there are no teeth there to prevent it from stepping past the range it's designed for and twisting up the springs.

Speaking of springs... yours look like they might be tangled up. That could be the cause of stepping problems.

If it's over counting bonuses, it sounds like you still have some issues in one or both of the bonus units. Bonus count up should work like this:
1. 1 to 10 bonus unit operates for two cycles of the score motor. It goes through the 1 to 10 relays and for each one of its closed (pin was hit) it scores 1,000. If it's open, then nothing scores on that position of the score motor. (Scoring will sound somewhat intermittent.)
2. If you have any strikes, strike bonus unit will cycle, awarding 1,000 five times per stepper position unit it reaches zero.
3. When both bonus units are zeroed, either the 1 to 10 relay bank will reset or if bonus is held, strike bonus unit will step up to its previous position.