6mm Rem is better suited for a long action, second you have to scrounge for brass in this caliber.
243 will not outperform the 6 Rem using less powder, as the 6 Rem will shoot any bullet accurately about 100 fps faster or more.
You can make 6 Rem cases from 7x57 or 257 Roberts brass easily, but you will have to neck turn the brass.
243 AI is a fantastic cartridge given match dimensions on the chamber with a freebore that will match your intended bullet, ie. don't put a freebore to match a 105g berger then want to shoot a 70g Nosler.
The 6Rem AI is a power wagon and a half, just don't screw up the custom job by putting it on a short action.
While or if you are considering customs, consider the 6 XC and the 6 SLR that are 95% of the 243 Win or equal the 243 Win with less powder, longer necks that give 1000 rounds more barrel life.
Having said that, the 243 Win loaded with 100g bullets and R#26 will be getting 3300 fps perhaps a little more depending on the barrel.