tr6, it makes a certain amount of sense, but the codes just aren't set up to handle that situation.
In a more general case, if a tank is not built to compliance to API-650 in the first place, there is no provision or procedure to go back later and examine or test it and certify it.
In your case, the only actual limitation would be that you are supposed to take shots more or less equally for all welders, with qualifying shots for each welder, and if you don't have records of who welded what, you can't do that.
Another limitation is that the builder is responsible for complying with the code, and if you uprated it later, you'd presumably have a split responsibility.
A similar situation would occur if you wanted to take an Appendix A tank and "convert" it to a standard-design tank.
A related issue is that if you calculate thickness based on a joint efficiency less than one, then logically, the required thickness away from joints would be correspondingly smaller, and repads could be designed differently away from joints, etc. I don't remember to what extent this approach is allowed in 650 or 653, though, but if allowed, it might accomplish some of what you're wanting to accomplish with the additional radiography.