Keith, I've had some experience of cutting out parts doubled on to 2mm hard card. It is indeed a lot of work, and in the end I resorted to a power table jigsaw.
However, since then I have been thinking and looking for proper substitute material for the hard 2mm card. The best I have arrived at is 2mm depron (which is the white foamy stuff they use for insulating electrically heated floors). I have not been able to locate a source for that, and in any case it is kind of expensive-ish.
Imagine my joy, therefore, when finding out that 2mm depron (or similar material) is used for protecting packages of large-sheet papers, such as available in artists shops.
You should try to locate an artists shop selling large sheets of expensive paper, like aquarel paper and similar, and kind of mention your problem. Perhaps they, like my shop keeper, will feel in a merciful mood and just give you the large sheets (which they trow away in any case).
Although I haven't tried them for a real model yet, they seem ideal. You will probably have to double them both back & front with ordinary paper (pattern on one side; suitably coloured or white, on the other) for rigidity.
The good news is that white glue works very well. The even better news is that you can make exact cuts, and the cutting is like through butter, at least compared to 2mm hard card.
For what it's worth. I'd love to see it tried out on a full build.
Leif