Well, to complete the circle, I rode this today (and, in the outward direction, on Wednesday). I used the route I outlined above, which was, on the whole, fine.
I didn't enjoy the A1065, but it's manageable if you don't mind being passed by HGVs. There again, coming back the B1102 had more traffic than on the outward leg.
I used the Santon Drove Road from Santon Warren to Croxton Heath. The most westerly part of that is a sandy track (the rest is metalled). Today, after some rain, it was a bit tricky on narrow road tyres, and I was slipping around rather. It was OK on Wednesday.
It's still the case that, as far as I know, there are no useful routes in the western part of Thetford Warren (and see above re sandy tracks anyway). There's a sign marking the obvious access to Shaker's Road as private.
I've written to my MP following a rather unsatisfactory response from the HA, saying that they didn't really think about bikes because the new A11 was planned a long time ago, when no-one considered that kind of thing. I still hold that not being able, for practical purposes, to get between Mildenhall and Thetford on any vaguely direct route is unacceptable.
Good ride though