I just called Allstate today and spoke with a local agent, who contacted the home office. Their story is that they sell trailer insurance as part of an auto policy, but that they do not insure custom trailers or vehicles of any kind for the "value-added" part. So they would do what my current insurance is doing, insure the chassis that I bought but not the part that I've added to the chassis.
I'll check with Farmers and State Farm.