Well, after a long time on the back burner, I finally got around to finishing this platter.
There were a number of useful suggestions (above) and also some very helpful advice from Terry Smart of Chestnut Products which I've partially copied below as there may be some useful tips in there for others:
"You've suggested a few alternatives, and the option to leave the oil to fully dry (should only be a few days) and apply a wax over the oil is the best one. I'd be inclined to use a fine abrasive (such as one of our NyWeb pads) to bring the surface to as uniform finish as possible, then apply something like WoodWax 22 and buff that up to the shine you want. It's possible to apply a couple of coats, or even use Microcrystalline Wax on top of it.
............
I understand your reservations about using the wax. A couple of suggestions to avoid those issues - apply the wax with a brush, something like a shoe brush, to avoid a build up in the crevices (that, say, a cloth could cause). Then, assuming it's our WoodWax 22, buff it up almost straight away using a firmer bristle brush (we sell these, or you can use a firm shoe brush). This should remove any surplus wax, avoiding the white spots.
Or, you could use our Medium Brown WoodWax 22, which will have minimal colouring effect on this piece, but doesn't dry white in concentration.
I'm not a fan of mixing oil types, they have different make-ups and don't always co-operate with each other when it comes to adhering properly. You would probably get away with it, but I'd do this as a last resort."
In the end, I rubbed it down lightly with a green meanie (from a floor polisher!), then went over it with white NyWeb to give a pretty good matt finish with no oil blobs remaining. Because the oil had had so long to dry, I then sprayed it with four coats Chestnut acrylic satin lacquer and it ended up with the colour and satin finish that I was after.
Not the usual approach, but it worked in the end, and I'd like to once again thank everyone who contributed their thoughts.
Duncan