Thanks guys and gals for all the advice. I decided to go for the no-finish finish. The photos show the result. I also refurbished the old pine chopping board, which had gone black at the ends (mould?).
I think the search technology on this board (!) could be improved a bit (google?).
Searches for historical consensus won't necessarily yield good advice, as this thread has shown, trends can change with time.
Incidentally, the jarrah board is two pieces edge jointed with aquadere polyurethane glue.