Here's my LH Savage.
That was when it had the factory 300win barrel on it. It was very accurate. Now it has a Shilen 7mmWSM that I'm just gettin broken in.
The stock is a Stockade Tactical/Pdog. Basically a copy of the A-5. The bolt handle is a Sharp Shooter Supply. They don't make them anymore, but there are several places that do.
Anyway, just because it is not a Remington doesn't mean you don't have the aftermarket parts to make what you want.
It might take a little extra time to find the LH specific parts, but their out there.