The states register vehicles, not insurance companies.
And while a big box insurance company might not insure a heavily modified vehicle, there are niche insurance companies who will. Or you could even self insure in a state that allows it.
I imagine it's not hard to get liability/collision insurance on a modified vehicle, and that's all you really need; most insurance will cover damages you cause on "any vehicle" you drive, so it doesn't usually cost much to add an additional vehicle unless it's particularly risky; that this has a real VIN and a real manufacturer should make it pretty easy. If you really think you need comprehensive insurance, you'd need to get specialty insurance anyway, because normal insurance is going to give you a near zero value on a car like that.
And while a big box insurance company might not insure a heavily modified vehicle, there are niche insurance companies who will. Or you could even self insure in a state that allows it.