Some info here:

http://www.pinwiki.com/wiki/index.php?title=ALI/Fascination_Repair

Are the connector pins clean and free of corrosion?

Does the game go through the playfield reset sequence?

Do you have the theory of operation guide? It is very detailed in listing the sequence of operations and what diagnostic lights should be lit on the boards.

Not the PCB edge connectors--the large square plugs.

If you have a lot of difficulty trying to seperate them, chances are that they are corroded and may need to be replaced.

http://www.pinwiki.com/wiki/index.php?title=ALI/Fascination_Repair#12-pin_Plug.2FReceptacle_Connectors

You really need to replace them. You can get the pins here: https://www.greatplainselectronics.com/products.asp?cat=2

Fix those before you start trying to troubleshoot logic/chip issues.

Where are you taking the measurement from? Directly on the regulator or on one of the boards? If it's directly at the regulator, that's too low and by the time the voltage reaches the boards, it will be even lower.

If the 5v is too low, the game will exhibit goofy behavior since it can't activate the logic chips correctly.

http://www.pinwiki.com/wiki/index.php?title=ALI/Fascination_Repair#Strange.2FMalfunctioning_Game_Logic_Issues

Unfortunately, the fixed 5v regulator is not available, so you have to replace it with an adjustable 5v regulator with additional circuitry or a 5v power supply (like the ones used in arcade games).

http://www.pinwiki.com/wiki/index.php?title=ALI/Fascination_Repair#5v_Regulator

It should be fine. The letters at the front usually signify the manufacturer of the chip.

First thing I'd do is backtrace the logic paths for what triggers the shoot again lamps.

I'd start with IC1 on the player up board.

You'll have to backtrace the logic and see where those paths take you. There are probably still one or more bad chips.

Does it tilt after you hit a coin switch, or tilt only after adding another player?

If after adding another player, I might guess something on the player up board responsible for the logic when the credit switch his pressed (starting at pin D).

You can also try setting up a camera to record the diagnostic lights on the border and slowing down the playback speed to try to figure out the sequence of operations leading up to the fault.

If it's tilting at random, first check all the tilt switches and make sure they are working properly and the screws that should be insulated from switch blades are actually insulated.

Then, backtrace the logic path for the tilt function through the boards and see what chips it passes through.

Any luck?