Hard to tell from the photo of your stator wingings but they look burnt in the dark area. If the windings have the electrical varnish burnt off, then that's the end of that set of windings. You'll need to have it rewound or replace it, which is likely much cheaper.
A failing stator winding would also fully account for your symptoms, including what happened when hooking the stator as the excitation source to the AVR.
Given your running environment is a bit corrosive, you might want to consider a better quality generator head for the replacement, one where the windings are sealed/dipped completely, unlike the ST heads. The best thing about the ST head is the price; they are NOT a high quality alternator. I use one for my off grid homestead primary AC power, where my typical max load is 2000 watts and my ST-3 has been reliable once I replaced failed bearings, failed diode bridge, added my own design AVR and got rid of the "doghouse". But I am in Arizona, and my engine and ST-3 are indoors in a dedicated engine shed; corrosion is not an issue. I also have a spare ST-3 on hand for parts or replacement. I am using it again on my neighbor's similar setup.
Hopefully Gary of Diesel Electric Service could suggest an alternator that might fair better in your environment. I'm just a hobbyist; his years and depth of experience/knowledge is awesome. I'm just guessing about corrosion being a factor in this failure.