There's no grey area with the Mini mentioned here. The monocoque has been altered and therefore it s no longer the vehicle that was registered in 1972. It's going to need to go through IVA.
The old regulations allowed cars that were radically altered to retain the donor vehicle's registration number. Effectively the only thing that was changed from an identity point of view was the make and model on the registration documents. Hence you see Z-Cars and kit-cars with old Mini or whatever registration numbers and tax exempt status.
If you can prove that this spaceframed Mini was altered and the DVLA (or even DVLC) were correctly informed in the days pre SVA (predecessor of IVA) then they will allow it to carry on with the current identity but if you can't prove it whether it really was altered back then or not then it's counted as new modifications and will need to go through IVA. The level of proof they require is exhaustive and very few people can manage this route even on cars that were legitimately done in the dim and distant past.
Once it's gone through IVA it will get an age related plate based on the age of the donor vehicle, if it's a single donor, or the manufacture date of the engine if it's multi-donor (but it won't get historic status and be tax-exempt if you use a pre '74 engine or donor). If you use all new parts (and can prove it) plus up to one major component re-conditioned to "as-new" then you can get a brand new plate as a new vehicle. My advice would be to try and work this to get as old a plate as possible because rightly or wrongly subsequent MOT's will apply the regs for things like emissions based on that date so if you've got an older engine (or a newer one on carbs) it may struggle to get through later emissions rules.
DVLA/DVSA - are a useless bunch. They don't understand their own rules and will interpret them differently depending on their mood or what they had for lunch - speak to two different people and you are almost guaranteed to get two different answers (and speak to one of those same people the following week and you are likely to get a third answer). If an answer is going to be critical to your build get it from them in writing. This situation is getting worse as the local offices have gone and you can no-longer speak to them face to face (you can't roll in and confront them with "last week you told me x and now you are saying something different"). The guys in the testing stations are far more helpful if you can get in touch with them (although you still get the odd dictator wannabe who seems to want to make life difficult because they can) - kit-car clubs often have a relationship with them and can sometimes put you in touch with someone who will actually be testing your car and can give advice about the required standards and how to navigate the process.
Iain