So all the transistor tests, wire traces, stuck switches, etc all check out ok?

Sounds like some major switch matrix problems. Firstly don't limit your testing to looking for things that have failed, who knows what the prior owner did to the game. I would inspect the entire game and look for previous work.

Check all the connectors and make sure they're installed correctly (in the right spot and not shifted over a pin). Can you get into diag? If you can I would remove the row and column connectors and then jumper from each row to each column and see if the correct switches indicate closed. Pinwiki probably has a procedure for this.

Note: You may have to power the game on and then pull the row and column connectors (not sure on a system 6).

If you can't get into diag I would start with troubleshooting the coin door switches. These can also be manually fired on the CPU board with jumpers also.

Edit: Also check the wires on the row and column connectors to make sure they're installed in the correct positions (the switch matrix diagram and cpu schematic will help with this).

Question #1 in fixing any system 3-7 game:

Have you replaced the 40 pin connector?

http://pinside.com/pinball/forum/topic/vids-guide-to-bulletproofing-williams-system-6

Until you check / replace all the connector header pins trouble shooting is crap.

I was just reading the matrix diagram for that game and if you already checked for missaligned board plugs its possible that somebody repinned the green wires and they could have gotten the grn-brn and grn-red wires transposed. If so you could get the exact effect as the jet bumpers would trigger as credit, credit and slam tilt. With a game running trigger top roll over A and the Outhole, if either triggers a tilt warning or tilt while the actuall tilt mechs trigger scores then start checking for the transposed or shorted grn-brn grn-red wires.

This sounds like a classic case of mismatched connectors between the head and playfield. I'm talking about the big 24 or so pin connectors. The only other simple thing I can think of is swapped connectors on the driver board. I think every header is 9 pins so if keys have been removed it would be easy to put connectors in the wrong place.

Just match the wire colors. Sometimes the connectors are not color matched.