I think that the red is awful since they 'tarmacced' it. Yeah, it was boggy in the winter, but I used to enjoy a soaking wet mud-fest through there. Suppose it's not for everyone now, although it's a bit of a cycling highway.
Agree that tyres are a bit of a compromise there, but there's nothing that tricky/slippy/rocky or whatever, that requires a very specific tyre.
mrben100, the Edge is good there when it's very gloopy but are a little draggy when it starts to dry out and not great over roots. They'll do the job though. Just don't pump them up too hard & they work better over the roots. I've never pinch flatted at Thetford so you should be OK.
If you have only ever ridden on the red & the black, it really would be worth hooking up with some people & having a blast around the singlertrack on the Brandon side. It's very flowy & much better fun than the red.
Or just park up in Brandon and have a morning exploring…..