I dropped a 35 Winchester shell in and it just about made it.
Seems the case shoulder is further forward than the chamber although the rim fits exactly when I put the shell in backwards.
I also compared the 35WCF base diameter to a 8X57JR and it is a bit smaller - looks like the right base diameter for my chamber.
At this point I am inclined to go the rebarrel route... probably to 400/350 Rigby.