I seem to recall that it used to be permissible to take an untaxed vehicle to the testing station, but that it was advised you should be carrying written proof of the test appointment. I would suggest you do not do this without written confirmation also from the DVLA.

The website has a "contact us" page.

Alternatively your local test centre are likely to have come across such a case before, and to know the way forward. I take it you don't have ready access to a cat transporter vehicle, that would certainly be one way to tackle it.