A Contender can handle the 270 Winchester, 30/06 or any other cartridge of similar diameter as long as you use VERY light loads. That said, I think it's not a smart thing to chamber a Contender for such cartridges since if someone seeing 30/06, etc. stamped on the barrel ignorantly tried to shoot factory loads in a Contender, damage to the gun or worse would probably result.
Of the 3 cartridges you mention, the 6.5x55 & the 9.3x57 would both be too high pressure for the Contender. The 444 Marlin cartridge is OK in a Contender as long as factory load pressures aren't exceeded.