My guess, and it is only a guess, is that the insurance should be on you--the driver/ operator. After all, you cannot ride all 6 mopeds at the same time, can you?
Company policies vary, at least in the old car hobby. Haggerty, I think, specifically addresses the issue for people who own more than one antique car as I indicated above--You can only drive one at a time.
Time for me to ask Nancy Jacobs for clarification. If I get a real ( as opposed to a "form) answer, I'll post it back here.