ORIGINAL: NVMIKE
If your lefty try the ruger #1's.
Now there's a bit of useless advice from a well meaning right hander. Mike, the Ruger is as right handed as they get. Try to get a cartridge into the chamber under a low mounted scope, under stress, with your left hand.
Carryin' a rifle with a 26" barrel is only useful in certain circumstances, not huntin' in heavy timeber.
The 788 was a neat rifle with a very stiff action and a fast lock time, but with the locking lugs on the rear of the bolt you couldn't load full loads. The bolt compressed and you had to use a small base die to get the brass to go back into the chamber. That reduced case life signirficantly.
Remington did make some lefthanded 700s but not very many, and evidently no one is willing to part with them while alive. If you'd like one haunt estate sales.
If you really want a left handed 6mm, buy a Savage with a worn barrel and put a 6mm barrel on it. The old style short action, called "J" by most owners would be fine, or one of the long actions with a short magazine.