Here are the switch states at the various positions:

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On the 100k drum unit, the 9th position switch is the omitted one. That's the bottom one on the diagram I posted.
So when the reel is in the 1-8 pos, both the remaining switches should be closed.

Lets adress the 100k Drum Units (DU) not reseting first.

Below is the portion of the schematic that controls the reset of your 100k DU. The fact that ALL your 100k DUs don't reset may point to the no3 Reset relay which is common to all the 100k DUs.
However the no3 Reset relay also controls the reset ot the 10k DUs. If the complete relay was not working then both 10k and 100k DU would not reset. Have a look at the no3 Reset switches anyway just to rule this out. Maybe 4 out if the 8 switches are messed up for some reason.

Another lead would be the zero pos switches on the 100k DU. Not sure if its the top or middle ones (no bottom ine on the 100k DU) , but they should both be closed when the 100k reels are NOT at the Zero pos. If any one is open, that would prevent the corresponding DU from reseting. Your post #1 seems to suggest one might be open in 1-8 pos! If true, that would be part of your problem.

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Just posted my answer above and realized you has solved that problem... good.

Now onto the next problem.
When you say you cant score above 10k, do you really mean that your 100k DU does not increment by one when your 10k DU rolls over from 9 to 0?

Here is the circuit that makes the 10k DU step up when the the 1k goes from 9 to 0.

If the problem happens for all players, then potential culprit might be the corresponding snow-shoe wiper on the player unit disk. Maybe it fall in between pads. But if that would be the case, you'd have other problems elsewere because all the pads would be misalingned. Check anyway.
Maybe wires connecting to the top strip of the player unit are disconnected. The ones in question here are 5, (affecting all players) and E, F, G and H ( affecting only the corresponding players). See pic below. (Working off my phone here. Uploaded it and later wanted to marked it up but can no longer figure out how to remove that one and replace it with the marked up one. Pinside changed the interface it seems.)

Can also be the contact on the 1000pt relay. More likely. Find the proper contact by refering to the wire colors. Red/yellow and red/orange in this case. Make sure it closes when the 1000pt relay energises. If it stays open, it wont step-up the 10k DU.

Last obvious resort (from looking at the schematic) is that the 9th position switches on ALL the 100 DUs remain open when reels are on pos 9. Unlikely, but then, that was the case for your previous issue.

Test these out. On stanby sitting in the bleachers here waiting for my kid to finish her lessons. Still have some time for another round of trouble shooting.

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Here is the added gray wire. Shown in blue on the schematic below. intent was to bypass the switch on the score motor that energizes the ball release coil. Certainly not a factory thing. But was Jerry-rigged for a reason. In general theae mods are often part of a larger mod and removing them often breaks the overall mod and messes up the game. I always remove those but only after i understand the big picture.

For now have a look at score-motor switch 4A (6th cam from the index cam, bottom of switch stack). Maybe it's defective and that's the reason it was bypassed causing the ball release coil to fire for the whole duration of the score-motor cycle. This would still allow the ball to be served but woud keep the ball release coil energized for long time and have it overheat and possibly fail. Could be the cause of your ball-not-serving problem.... Check the ball release coil.

On your pictures of the outhole relay, i notice an other gray wire on one of the lugs of the outhole relay's coil. Cant see where its going. Looks suspicious . Unless its simply a jumper to the next relay beside it.

The green and blue wires look normal. Just jumpers to the other switches common lugs.

See pic of my machine. I can get a better one when i get home.

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Another path to explore regarding your 1k relay machine gunning and locking your 10k relay.

The normal sequence of events is this:

1) 1k relay fires and relay switch at E22 in self hold circuit closes thus keeping the 1k relay energized thru the normally closed EOS switches of the four 1k DU EOS switches. (Red)
2) At the same time, relay switch at C11 closes and energized the coil of the 1k DU thru the player unit. (In Blue and shown for player 1 only). This sets the plunger in mouvement and the reel turns by one unit.
Eventually, the plunger hits the 1k DU's EOS switch and opens it. This switch is in the self hold circuit above (red). So the circuit breaks and the 1k relay de-energizes.
3) also, if the 1k reel happens to be at its 9th pos, then what i show in post 14 above will also happen ie: 1000 re switch at E22 closes and energizes the 10k relay thru one of the 9th pos switches.

Where this could go wrong:
A) if one of the EOS doesn't open when hit by the plunger then the self hold circuit (red) doesn't break and the 1k relay stays energized.
B) or it opens, but just barely and keeps arcing essentially opening and closing rapidly. This would cause your machine gunning.
C) could this lock your 10k relay? Sure could, depending on the relative gapping of the various switches on the chattering 1k relay.

So check your EOS switches on all four of your 1k DU.
Might as well check the gapping on all EOS switch on all 20 DU.

Screenshot_20190106-201913 (resized).pngScreenshot_20190106-203012 (resized).png

The various switches on the drum units are often the source of many startup issues. They need lots of TLC cuz the DUs are one of the most used items on old EMs. Specifically, the player one as you mention.

May contact you via PM to get a few pics of your GP if you dont mind. Completing some work on mine and need some reference pics.