Cool project, I'm working on fixing up my Space Mission that hadn't been played in 30 years. I've spent an unhealthy amount of time studying the schematics in order to understand the flow for troubleshooting. Just the other day I finally got it working 100% (hurrah!) - here is the expected order of operations when pressing the credit button in a game over state (Space Odyssey should be pretty much identical minus the player 3/4 support):

1. Credit button pressed triggers credit unit reset (to remove one credit)
2. Credit unit reset EOS enables the coin relay to fire, which starts the score motor (it will continue running as the relays below fire)
3. Coin relay active and game over active causes the player 100,000 latches to fire (clearing any previously-tripped 100,000 lights) and also fires the reset relay
4. Coin relay active and score motor cam 1 toggling causes the following to fire simultaneously - total play meter, coin unit reset (resetting it back to a single player game), game over relay latch (taking the machine out of the game over state), ball count unit reset (resetting it back to ball 1), player unit reset (resetting it back to player 1)
5. Reset relay active and any score reels not being at zero causes the player 1-2 and 3-4 reset relays to repeatedly fire on the score motor impulse / impulse forward cams (5 times per half revolution)
6. While the above is happening, if the bonus unit is not at its zero position then having the reset relay active will cause the bonus relay to fire
7. Bonus relay active and bonus unit not at zero causes the bonus unit reset to fire on the score motor impulse cam (stepping the bonus down 5 times per half revolution)
8. Once the bonus unit hits its zero position, the outhole relay fires
9. Outhole relay active and score motor cam 3 toggling causes the bonus unit to step up (resetting it back to 1000 for the turn)
10. Outhole relay active and score motor cam 4 toggling causes the ball release to fire (sending the ball into the shooter lane)
11. Score motor cam 5 toggling cuts off the outhole relay and the score motor stops

With the above in mind, you can observe your game and see how far it's getting. From your description it sounds like it's getting stuck around step (6) in the bonus unit reset process. Which lines up with you saying the flippers/bumpers/scoring don't work - those get cut off if the reset relay is still active. And one of the things that keeps the reset relay active is the bonus relay being active. This also lines up with you saying the outhole relay is doing nothing - it won't fire until the bonus reset completes.

What do you see the bonus unit doing during the reset process? Is it trying to step down? Does it ever reach the zero point? If you can confirm how far it's getting in the steps above, we can work from there.

The manual is probably the closest you'll get to documentation on the various relays/solenoids/switches. I do agree that some of the names are vague and only give you a loose clue as to what they do (like "COIN" or "BONUS"). But once you get used to tracing the schematics, it will become a little easier to see what they do. Especially since a lot of games, even from other manufacturers, use similar naming conventions for everything .. so you can read descriptions and threads about other games and it will usually be similar for your game.

This is normal and actually a good catch - I should probably throw this somewhere in the startup sequence I posted before (around step 6, although it will actually happen almost right away when power is applied and the ball is sitting in the outhole). The reason for it is that the outhole switch being closed provides a path to fire the bonus relay as long as it's not already at its zero position:
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Once the bonus relay fires, it will cause the score motor to move and also close a switch that will lock itself on until it hits the zero position:
04 (resized).png
02 (resized).png

When the bonus unit hits the zero position, the bonus relay will de-energize and the make/break switch below will toggle to try to enable the outhole relay after the score motor stops (step 8 in the startup sequence above). But at this point the game is still in the game over state .. so the outhole relay logic won't fire.
03 (resized).png

Note - When reading the schematics, for the most part the switches are shown as if a one-player game has been started. So that is why the game over relay switch above is shown as closed .. but in the case you're describing, it would still be open (since power was just applied and a game hasn't actually been started yet).

I verified on my Space Mission just now that if the bonus unit is already at zero, then turning on the power does nothing and it goes straight to game over. If I manually step up the bonus unit and then turn on power, it steps down the bonus unit and then sits at game over.

I would suggest slowly walking through simpler chunks of the schematics, and using the test light to see how/when things fire. I would agree it sounds like your bonus unit is stepping and resetting correctly .. so you're headed in the right direction. Let us know if you have more questions, or figure out something your machine is doing that isn't in the expected startup sequence.