I have a RH 6.5x284 built by Bryant with a long Remington action(trued), a 28" Hart barrel (I think heavy Palma), and a McMillan A5 stock. The trigger is Remington, but tuned by Bryant. I will have to look at the round cout, but pretty sure it is below 300 and may be below 200. It shoots 1/3 MOA (140 AMAX) out ot 400 yards, which is as far as I have shot it. It is tight necked, so neck turning is required. I have 20 to 30 prepped brass that is once or twice fired.
I know you said LH, but you may not find one. $2,000 plus shipping. Load developement is done for the 140 AMAX.
I also have a 260 Remington that is a short action trued with a McMillan hunting stock and a Shillen 22" or 24" fluted barrel and trigger. It is Remington light varmint contour. It will shoot 3 shots with 125 Nosler partitioned into a little over 1" at 200 yards. It has around 160 rounds down the barrel and is RH also. $1,800 plus shipping.
I can get you some pictures tomoorow if you are interested. Good luck in your search!