I would start by approaching the specialist insurers, of which there are many, but the likes of Adrian Flux, Footman James, MSM, Hagerty.
Because they deal with both modified and kitcars they are more open minded.
They will be keen to know that you are building it yourself as in their eyes you are far less likely to be ragging it about the streets in the way insurance companies have gotten used to with your normal new driver.
Best of luck
Steve
ETA The above insurance companies are well aware of Q plates and it means nothing to them.