I wouldn't worry about the 30V on the anti-cheat. If you are just measuring across the terminals when the relay is unpowered, you will see "phantom voltage".  The wire 78-4 end of the coil isn't connected to anything, so your meter has no valid reference point to determine a voltage value and the tiny current flow induced by the meter will produce a reading.

if you want to check the anti-cheat closing circuit, manually lift switch stack 5 on the timer cams and it should power the relay. If it doesn't, you can measure the voltage across the coil while holding up the stack or wedging some folded paper under the stack. If less that 52V, you can probe the circuit up thru CU 5C and the two EB trip relay switches to find the bad connection.

showtime (at least some of them) has a circuit at schem I7 that will close the shutter if the selection feature unit is not reset and the anti-cheat relay is not powered. If the selection feature unit open at zero switch is not opening (unit not resetting, zero switch stuck closed) and the anti-cheat is not powered, it's normal for the shutter to close.

if the start relay is staying powered because the timer cams aren't spinning, it's normal for the shutter to open.

so, check the selection feature unit is resetting all the way and the switch is open at reset. That should stop the shutter from closing. Then deal with why the timer cams index coil isn't powering...a switch on those cams powers the anti-cheat. If the mixer latch coil isn't powering either, the problem is not the coils.

don't forget to check the plug connections between head and cabinet/playfield - ideally unplug the game from the wall, yank the plugs, clean off the black crud from the inside/outside sections of the pins (the pins only contact the sockets in a couple spots), and squeeze along the length of the sockets hard between thumb and finger to bend in the tabs a little. You want plug insertion to require a bit of oomph to ensure a reliable connection.