I have the same problem with my 7.4 L with Thunderbolt V ignition. After changing everything and putting on a new coil it still cut off. Soon after it backfired and would not start again. I started swaping parts with the other motor and found it to be a bad ignition control module. I hope that is not your problem as the part is pricey. I am looking for a used one now. Part number 806961-2. It is shown in your first picture.

yea, kind of funny, but thats what i thought it was all along but figured i would do the like big tuneup of small cheaper parts first, this week we are going to hook it up to controls and take the rest of the boat out of it, and if it does it, i guess i have my answer... i don't know what my cost would be on it, but from when i looked it up in midas it was pretty expensive

did yours only do it under load actually running the boat or even on a hose on land?

While underway the port motor would shut down without warning. It restarted easily and I made it back to port. Once in the slip I tried to restart but there was a huge backfire and the motor would not start. I did all the tests for bad fuel, clogged filter, and bad gas but determined it was ignition. I even purchased a new coil but that did not fix the problem. I started switching parts and finally determined it was the ignition control module. I have found the prices range from $485 to $425.

How about ignition switch or connectors on under dash wiring. Also cannon plug on the engine. Good move to eliminate these things for the next test. Also a remote fuel tank can help sometimes also.

cannon plug is good, actually, while on land, i was wiggling everything i could, and could not get it to do it, appears it is only while under load... but like i said we will remove the "boat" from the test.

bajasport, when you said yours cuts off and then you have to restart, mine, does not turn off, just cuts out for a split second, and then continues running. very weird

Its pretty easy to pull the can plug and run a hot wire to the ign , and use a remote starter to turn it over. That will eliminate the boat.
I have seen the tach do things like you are describing, the reason it needs to be drove it the tach is getting bounced around when you are running the boat on the water and not so much on land.
But first eliminate the boat that will narrow it down.
Good luck

actually, as an update, something was happening with my key switch, but we also replaced the tach as it was being a little funny at times.

boat finally has no more ignition/electrical issues