Welcome to the wonderfully frustrating world of long range hunting for left handed people
I anticipate the day they offer a true LH version of the LRH, as I will probably end up with one of each... but until then, there is no compromising for me, I purchase LH only. (I really want the 6.5 Creedmoor)
Savage does have a "custom shop" & from what I hear, they are more than happy to build you what you want. Although if you are willing, I don't see why you couldn't switch the thumb screws to the other side of the stock, I held a LRH in 6.5x284, but I can't recall the details of the cheek piece.
You can always pick up another model in your chosen caliber & change out the stock, Savage has an outstanding reputation for accuracy, you don't have to be super picky.