OK, so doing a little digging around, there was an update to the ABYC rules that addressed that "safety ground" wire from the case of an inverter or battery charger to the boat's negative buss (or an engine ground block, which should be the same potential). It's still hard to wrap my head around the failure modes that cause a need for that, but that's a different subject.
NOW- ALL THE BELOW IS POSTED WITH THE CAVEAT THAT THIS IS BASED ON A MISSING CONNECTION. IF THAT IS THERE SOMEWHERE, THEN WE CAN 'SCRUB' THIS POST!
For your boat, I updated that diagram to what I think you're describing. This might make it easier to see what I'm talking about. This also explains the weird voltage you read (the 15VDC) and how that's possible. If you look at the simplified diagram below, I think it has all the key components. I think you said your isolator #4 connection goes to the inverter DC switch instead of the battery post, but that's a moot difference for this discussion.
If you look at the diagram, find the purple arrow. There SHOULD NOT be a connection between those two yellow lines at the case, although they should be at the same potential. The safety ground goes to the case, which (according to the ABYC rules) should NOT BE connected to the negative battery input on the inverter. The negative input on the inverter is connected to the inverter battery bank negative, so the inverter gets power. However, there is no connection from the inverter battery negative back to the engine grounds or the negative posts for batteries 1, 2, or 3. Therefore, there is no "reference" of "zero volts" at the negative post on the inverter battery. While you can measure a voltage at any of the batteries, that measurement can be different depending on which battery or what source you use as the negative connection for the meter. NO CURRENT can actually flow from the alternators through the isolator and over to the inverter battery, unless there is SOME OTHER CONNECTION that is not shown in the diagram that connects the negative of the inverter battery back to either the engine blocks or the negatives of batteries 1,2, or 3.
Ironically, since there that connection doesn't exist, your "safety ground" is essentially useless, as no current can possibly flow there and get back to the inverter battery bank. EDIT: as I went to post this, I saw you had posted some additional info. The answer on the location, is that it needs to tie to the negatives on the other batteries, or the engine blocks... if you have a "negative buss bar" that would be a good place. The size would be "bigger is better", but it would also need to be at least as big as your "safety ground wire", as it would now be part of that circuit.
Inverter-wiring-customized.jpg
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