First, I don't consider the .375 a big bore; it is a medium bore. However, for the purposes of this discussion, we'll let that slide.

Second, the .375 is adequate for thick-skinned DG hunting, but it is not considered a good stopper.

Third, forget Ruger. They don't offer any LH rifles in calibers above .30.

Fourth, what is your budget? $700? $1500? $2000? $5000? $10000?

For $10000, you can have Butch Searcy build you a left-hand double rifle in one of the Nitro Express rounds (e.g., .450/.400, .450, .470).

For $5000-6000, you can buy a LH Dakota 76 Safari, or have a truly fine custom rifle built by some of the top gunbuilders.

For $2000, you can buy a NIB LH Winchester Model 70, and have it re-barreled and re-worked into a bigger, better gun (e.g., .416Rem., .458 Lott, .470 Capstick).

For $1500, you can buy a Model 70 .375, and have it 'gone over' by a 'smith who knows how a DGR is supposed to feed and extract.

For $700, you can buy a used rifle, and shoot it while waiting for funds to re-barrel.

George