The 2003 Handloaders Handbook lists 2 rounds
1) 240 Gebby Super Var
2) 240 Gebby Belted Var
There was a lot of interest in the 50's & 60's in .243 / 6mm loadings. The 240 Gebby Super Var is based on a necked down 30-06. The 240 Gebby Belted Var used the 284 Winchester with a belt ala Weatherby.
P. O. Ackley has the 240 Cobra which was the 220 Swift necked up to 6mm.
Your best bet is going to be a cartridge cast. The rounds were high pressure loads.
I got caught in the 243 / 6mm trap. Had a custom rifle built based on the 6mm Remington. Had no thought at the time that 243 Winchester would become as popular as it did.
Pete