Didn't hear from you last night so I have some more ideas. If I understood you earlier you said you checked the battery red lead at the starting solenoids along with the red alternator high current output terminal also at that solenoid stud, and possibly a couple or more smaller red wires going off and doing housekeeping chores in your engines.
That being the case your alternator should be hooked up as it should be to your battery for charging purposes and the voltage measurement I mentioned last night isn't really necessary, although it is a data point.
The simultaneous engine problem keeps eating away at me. Gotta be a common thread.
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The engines connect to a dual throttle/shift control assembly, correct? The assembly has 2 separate key starter switches, correct? Each has a purple or red with a purple stripe that goes back to the engine to excite the respective alternator along with roughly 8 other wires in a plastic covered harness and that wire is connected to the respective ignition switch on/start terminal, correct?
The fact that you can energize your starting solenoids (red wire with a yellow stripe probably) and start your engines says that your ignition switches have 12v applied so we aren't going up there chasing 12v. You aren't going to have 2 switches fail on the same terminal simultaneously at 300 hours under most circumstances.
Therefore I can't point to the controls or control wiring as a possible culprit.
Your onboard charger, is it a set of 5 ampere chargers in the same housing, common, but individual isolated outputs for each battery? You already said that they will satisfactorily recharge your batteries when plugged into 110V so one has to think that they are performing normally and that they are always connected to the batteries via terminal lugs under the wing nuts on the battery terminals so there isn't a problem with cross talk between them and the engines alternators.
Ok, let's do this. Charge up your batteries with your onboard charger or shop charger. Once all are charged, disconnect your engine batteries from everything but the single red wire that feeds starting current to the engines starting solenoid input stud and of course the black - wire is still connected. I'd wrap the terminals you take off with electrical tape to ensure that battery #3 doesn't accidentally get hooked to them and they touch a ground somewhere and cause a spark.
Take your voltmeter with you and go to some water backing your trailer in like you were going to launch but don't. Crank one engine at a time and with the throttle above 1k rpm, check for 14v give or take at the 12v distribution point, the input stud of the starting solenoid. If you don't have it, do as Fazt mentioned and check your red/purple stripe or purple, whichever at your alternator for 12v. Is there any way that your drive belt or pulley on the alternator could be slipping? Is the drive belt cogged or just a plain vanilla v belt. What about the tension?
If you have 14v at that solenoid input terminal the engine is ok and you have something down line draining the batteries. I really find this hard to stomach as you have a 60 amp capability and at 12v you are looking at 720 watts of power going somewhere if you can't show any kind of charging voltage increase while running. The output current wire from the alternator is probably a #8 and if it were running 60 amps for any length of time it would be warm or worse to the touch.
Back to the nagging sensation....both engines are doing the same thing.......just doesn't make sense. No smoking gun??????
After you finish one engine do the other.
If you can get your engines to charge with the other batter(ies) wires disconnected, and have a fully charged #3 battery, since you are there why not make a day of it and worry about what's wrong when you get back. Will one storage battery last you a days outing? One word of caution here is that the alternators are made to keep a fully charged battery charged. They are not designed to charge a discharged battery. So if you run your #3 down, don't swap batteries with an engine start or you can overheat your alternator.
Ok, will wait for this answer.
Good luck,
Mark