Bedlam wrote:
I question replacing the outlets since they work fine on shore power and only pop under generator power. 
I know that Bedlam is very knowledgeable about these things, and normally I would defer to his expertise; however, because I didn't have a clue why my gfi outlets were tripping when I used the generator, I thought it would be prudent to get it from the horse's mouth--the guys who build 'em.  As soon as I told Randall at Host what the issue was, he replied:  "I'm glad you called; we had a run of defective gfi outlets; I'll send you three new ones today; that should fix the problem."  They arrived two days later, and yes, folks, that was indeed the problem.  Haven't had any issues with them since.