The anti-cheat is operating as expected - it should be able to latch if there are no replays on the register. It is initially powered through the start relay, which pulls in with your first coin. If you don't cut the power to the game, then the anti-cheat will remain powered and latched throughout gameplay.

So that behavior, at least, is normal.

For your shutter motor constantly running - it does sound like it's dropping to tilt (but that's normal on first power up).

Your shutter motor will open when the first coin is dropped, and remain open until your first ball leaves the gate. There are a few switches to check on the shutter and under the playfield.

First, the switch closest to the shutter motor is the motor runout switch. If that never finds 'home' then the shutter will never stop moving. Another is the set of switches actuated by the shutter board itself on the bottom right side of the playfield. If they are not fully changing state, or the metal arm has become a bit loose, then the shutter will not sense that it is fully open or closed.

I would suspect those first as the other tilt-like behaviors sound normal.

Also:

This is absolutely true. You may have unintentionally borked up some switches just lifting the playfield or setting it down.

30V at anti-cheat is incorrect. That is tied to EB trip relay #1 and CU cam 5 switch C (third from the bottom).

If you don't have 50V through that circuit, your anti-cheat will not latch.

You trip bank continuously resetting is because your shutter motor keeps opening. That hits switch 3B on the shutter which will fire the reset coil on the bank.

Timer unit comes into play when it lifts the first ball. I believe your problem is before the timer unit.

Your start relay should not be holding in in normal operation. That might be caused by a stuck switch in the replay reset relay (in the same area as the start and anti-cheat).

Sorry for the delay in responding, I must've forgotten to hit submit!!

Ha! Left out the timer cam index switches because 'surely' those weren't the problem. Thanks @baldtwit!

And regarding the plugs - yet another assumption on my part. Be sure to follow the above advice all the way through and you will find your problem.