I agree with Savage having the best selection of LH rifles,I have 5 of them as well as a couple RH.
If you can't find what you want from Savage,then you can build an even better rifle just using any Savage action.It only takes a few minutes to assemble a complete custom rifle if you have any knowledge of firearms,and the correct tools-An Action wrench,Barrel nut wrench,and some Go/No Go gauges.
I really like the Accu-Trigger,but don't care for the Target Accu-Trigger.It's very sensitive,and if you don't set it up correctly,it is very dangerous. I prefer the SSS Competition Trigger over the Target Accu-Trigger,and it can safely be turned down from 2lbs-12oz.
Here's a few of mine-
In front-Savage 110FLP 25/06 in a Choate Tactical stock,Ken Farrell base,Burris Signature Zee rings,Sightron SIII 6-24x50 LRMD scope.
Back-Savage 10FCP 308 is the same set up as the 25/06.
I bought this gun used- Savage 12FLV 308
A before Pic- Factory set up with 2pc bases and a Redfield 4-12x50 scope
After I changed it to a 7mm-08 with a Savage LH laminated Target stock,Tactical bolt handle,26" ER Shaw varmint contour barrel,Weaver rail base,Burris Signature Zee rings,and a Swarovski Pro Hunter 4-16x50 scope. I also have a 6.5 Credmoor barrel for this rifle,until I find another action to put it on.