I'd have some brass to use for that idea.  I have a couple Japanese type 38s chambered for 6.5x257Roberts.  I have S&B 6.5x57 ammo that I have sized down using the rifles.  Still, wouldn't it require an improved configuration to clean up the .243 chamber?,  Unless it's setback.  I don't imagine SAAMI .244 pressures are any lower than .243, so I'd still have the same hot factory ammo problem.

However, right now I have the barrel seated to the point that the bolt will just close freely, it appearing to me that the boltface contacts the breechface, leaving no fore and aft play as the guide rib contacts the receiver.  Closes the same on a full length sized case, but if let down slowly on a once fired and unsized case (likely fired in a Handi-rifle), it doesn't go all the way down on it's own.