Problem is, the primary will invariably be the innermost of the windings making access difficult.
Depends how neat a job it needs to be. First thoughts would be to replace with 2 transformers, as you say. The likelihood is that most of the power will come from one of the windings, meaning the second set of voltages can be provided by a very small transformer (likely feeding preamp or driver stages).
If you need to do a much neater job two thoughts come to mind:
1) There are companies who will wind one-off transformers to your specifications for not too much money, but obviously more than an off-the-shelf one.
2) Someone (RS?) used to sell bare transformers with just a primary winding so you could wind a secondary to your specifications.
I just bought a couple of toroidals from Rapid electronics for a Hi-Fi DAC I've just built and they have a very wide range, reasonable prices and they look to be nice quality transformers.
Kevin