In the shotgun world the answer is to use a "crossover" stock, for scope use on a rifle then a stock can be made or modified to suit.
I know of at least one shooter who shoots bell target right handed with a diopter using his left eye simply by removing the adjustable cheek piece from the stock and resting his chin on the cutout section of stock. This could easily be applied to a scoped rifle especially one that already has an adjustable cheek piece.
Using offset mounts with a scope will mean excessive crossover problems at ranges other than zero'd range, I would suggest that if unable to shoot left handed then the head should cross the stock to use a centrally mounted scope, I can't imagine shooting HFT with approx 65mm left offset on a scope! It would be no problem with fixed range competitions such as bench rest.