I presume the MPU board has suffered battery corrosion in the past?

Does the problem occur when both J2 (playfield switch harness) and J3 (cabinet switch harness) are disconnected from the MPU board? (you can disconnect them live).

If yes:
Switch the machine off
Leave both J2 and J3 connectors disconnected from the MPU board
Grab your multi-meter and connect the black meter lead to ground.
Set the multi-meter to measure resistance, if your meter is not auto-ranging, set it to 200k ohms

With the red meter lead, measure the resistance on pins 1 to 5 on MPU J2 pin header. They should all read around 56k ohms.

With the red meter lead, measure the resistance on pins 8 to 15 on MPU J2 pin header They should all read around 56k ohms.

Report back any substantially lower readings and post clear pictures of the MPU board.

If you disconnect J2 (playfield harness) from the MPU board and it still reports #07 (tilt) in switch test mode, how do you know the cabinet tilts are working? Did you also disconnect J3 (cabinet harness) to confirm the problem is on the MPU board?

See post #2 above.

See post #3 and #5 above.
If disconnecting J3 from the MPU board cleared the tilt switch closure, then the next step is to cut one leg of the capacitor at the plumb bob tilt to disconnect the capacitor from circuit. The capacitor may have a partial internal short.