Update: So having attacked some scraps with a sander, we discovered that we could relatively rapidly get a really smooth finish. Using a belt sander (36 grit) to roughly clear the saw marks and generally roughness, then two passes with a random orbit. One (40 grit) to get rid of the parallel grooves from the belt sander and a second (120 grit) to buff to a smooth finish. In places that the belt sander can't reach (such as around pegs, or the joists that are already in place) a little more effort with the orbital sander will clear them. One or two tight corners (braces joining posts / beams for example) will have be finished more slowly, possibly by hand, but these areas are relatively small and thus the task is not insurmountable. Once the whole frame is sanded and the dust has settled it'll be oiled. Probably with linseed unless someone can produce some truly compelling arguments in favour of tung oil (I can buy tung oil, but it's not so easy to get hold of, linseed oil comes in 5L in every DIY shop and some supermarkets!).

The finished surface doesn't have the glassy smooth shine of a well planed surface (although the extremely squirrelly grain of the DF makes that a challenge anyway), but it does have touch appeal. The test scrap is currently sat in the house and it's hard not to brush your hand against it as you pass! :-)