This is a historical problem that will never go away and many genuine enthusiast are caught-up in it.
My only advice is to do the best you can under the circumstances.
To put it another way , make sure the car is insured for what it is NOT what the V5 says.
So, if it's a Spartan chassis running a Cobra body and a V8 engine tell the insurance company it's a Spartan chassis running a Cobra body and a V8!! The insurance companies aren't stupid and if they wont insure it you can't drive it.
.
Nothing is going to make it right and nothing will make an in-correctly registered car totally legal.
One of the main things to worry about is Road tax! It you running a doggy car and have claimed free "historic" road tax you are committing fraud, because you have knowingly de-fraud HMC out of the cost of the road tax, it you get "caught" they will prosecute you for fraud and that's serious !!
DVLA are now trying to shut-the-door on this practise, but the DVLA system was, is and will always be a mess as it's a government institution run by people who don't have a clue about the real world and who are answerable to no one .
At least VOSA have rule and stick to them!!!
Basically if you think or feel all is NOT correct, DON'T buy it, DON'T build it and finally DON'T drive it.
The police has had an amnesty on guns so why don't DVLA have an amnesty on V5's !!!!!