The DVLA has accepted my bid to re-register the Z3 as an electric vehicle. Hoorah!
I initially sent in my V5 along with a V70 form and the receipt for the electric motor, along with a covering letter explaining what I had done to the car. They responded after a few weeks with a letter asking for more information and photos. They also sent me a form for a ‘rebuilt’ car but I didn’t fill this in, as my car is largely standard apart from the motor and ancillaries swap. I emailed back some more receipts (inverter, battery) and some photos, along with more detailed information about what had been changed. A week later, back came my revised V5. That was it!
It’s much harder to change the registration on later vehicles, after 2001. Though the evidence from the forums suggests it is possible. Not an issue for me though.