Looking for good marine electrician on east coast

These guys have one of the top reputations in the area: https://www.wardsmarine.com/

I deal with a boat that has a GFCI on the main shorepower breaker in the boat, I've had it trip if A/C water pan got clogged and full of water.....or with an ice maker when the compressor was starting to go bad.

With everything off, turn off every single A/C breaker in the boat, then turn the main breaker on, then turn each individual breaker on until you find the circuit that trips the GFCI on the dock.

As for a marine electrician in Savannah, I do not know. Perhaps call Thunderbolt boat yard and they might have one working for them or can refer you to one.

I'm going to make a few assumptions, based on my understanding of what you are saying in your OP:
1) everything in your electrical system works fine when connected to a shore outlet which is NOT protected by a GFCI device;
2) the same goes when you are connected to the onboard generator, or if you are drawing AC from the inverter(s);
3) you do NOT have a master GFCI device onboard, downstream of the main breaker.

If the above is correct, I would think that there is indeed something wrong with your boat, and you just didn't know.
As a premise (which I'm making just in case), GFCI devices are meant to sense any circuit imbalance, potentially created by an accidental current leak through a human body, anywhere along the electrical circuit. In which case, by cutting the power immediately, a GFCI device can actually make the difference between life and death.
Now, the most common standard in Europe for these devices is to cut power at 30 milliamps of current leak, but I'm not sure about the US. There are devices capable to sense leaks as low as 10 or 5 mA.
Trouble is, even 30 mA is actually a pretty small leak in absolute terms - not to mention 10 or 5.
On the other hand, the device MUST cut power immediately upon a small leak, otherwise it wouldn't achieve its purpose of protecting from severe electrocution.

So, let's say that your socket in Titusville marina is protected by a 10 mA GFCI device.
If my initial assumptions were correct, you might have always had a total leak of say 12 mA, and that is enough to trip the 10 mA device, even if everything works perfectly whenever you are connected to a non-protected shore power.
And mind, your 12 mA leak could well be due to a sum of several different leaks, like 4 mA in the cooktop, 6 in the heater, and another 2 elsewhere (it's almost impossible to have zero current leaks, in any somewhat complex electrical circuit).
For this reason, it would be appropriate to have a master GFCI device also onboard, to protect the whole electrical circuit also when powered by the genset, and regardless of whether the shore power is protected or not.

Back to troubleshooting.
The leak is obviously downstream of your main breaker, otherwise the shore power would trip off upon step 3 of your list.
This rules out not only the shore power cord, but also the segment of your electrical circuit that goes from the cord to the electrical panel.
Which is kind of a pity, because often the culprit, in boats where the power cord is attached to an onboard external socket, is in the socket itself, that can get wet inside due to weather exposure.
And in this case, it's just a matter of opening the socket, dry it out, and possibly use some spray electrical insulating sealer.
But this should not be the case in your boat.
So, what remains to be checked is which segment of the circuit generates more dispersion.

Now, I agree with Capt Ralph when he mentioned the "step 5" which is missing from your list.
In fact, I suppose that before turning on the main breaker in your step 4 you did NOT turn off all the single breakers downstream of it.
If you did, there's no logical reason why the shore GFCI should trip off, and that would be very weird indeed.
On the other hand, I don't agree with Pascal when he suggests that it's necessary to physically disconnect all appliances.
A GFCI device should not trip off unless there is a current imbalance, and there can't be any when a breaker is off, even if single pole (which imho should have no place on a boat, anyway), because there is no current absorption at all.
So, assuming that the shore doesn't trip off if you turn on the main breaker with all other breakers off, it should be sufficient to turn them on one at a time, to identify one culprit.

Mind, I'm saying ONE culprit because you could as well have more: in my previous example, if you disconnect the cooktop with its 4 mA leak, you would still have 8 mA residual leaks (6 in the heater + 2 elsewhere). Not enough to trip the 10 mA GFCI device, but the 6 mA leak in the heater would still be worth fixing.
But for this type of troubleshooting, it's necessary to open the electrical panel, have a leakage clamp meter, and know how to use it.
I can explain this further if you are interested, but that's something better left to a specialized electrician.
Also because, to complicate things further, the leaks I previously used just as an example can actually change, depending on whether the connected appliance is turned on or not, and also other factors like the relative humidity in the air - go figure!

Sorry for the long post, but I hope it can help.
Good luck, anyhow!

I know all the Navigators usually had Galvanic Isolators installed and a fairly clean and robust grounding system. But I imagine the dealer or aftermarket electronics guys have tapped into the factory wiring at some time. Best get a savvy electronics onboard to walk you through the process.

This is very puzzling ideed.
In principle, in a properly designed electrical panel, in between the main breaker and each line-specific breaker there should be ...ermm... nothing!
I mean, after the main breaker you should have simply some shortish wires, feeding each of the downstream breakers.
In best designed panels, this is often done through connecting bars rather than wires, but that's just a detail.
In any case, it should be practically impossible that any current dispersion develops just by turning on the main breakers, with ALL the downstream breakers off.

This leads me to think that either the electrical panel was not designed with these basic principles in mind, or someone played with it afterwards and made some changes/additions to the connections.
And since I have no reason to doubt what PB said in his last post about Navigator boats usually having a clean and robust elec system, the latter of these two alternatives seems the more likely.

Either ways, not something for which you can get any further help from anyone through a forum, I'm afraid.
Next step is bound to be have someone who knows his onions opening the electrical panel and putting his eyes and hands on it.
Just a hint: if he doesn't show up with a leakage clamp meter (which shouldn't be such an exotic tool for a good electrician, but I've seen some of them who don't have one, just because somewhat expensive and not so frequently used), look for someone else.

Check your shorepower wiring connections from the cable to where it attaches in the boat and at the back of the breakers. I've seen many that were loose after years of use.

I would suspect that if the boat has a Grill and/or Washer/Dryer than you have 240VAC Appliances onboard, you would typically see two 120VAC legs tired together on the AC Breaker Panel.

In my case it was the old style galvanic isolator 2005 had an issue and tripped the new St Aug marine power pedestals. Electrician disconnected the wire on the old isolator at the marina and all was well. Got home installed new galvanic isolator about $300.