My advice: Get an AR-10 or similar. The answer to many of life's questions is to buy another gun.
At first I thought - man, this is crap, that's not what he asked. Then I realized. dang, you're right. Just buy something with bottom metal and go from there. Nothing else is really practical.
Actually, nothing the OP can do in terms of a serious "make-over" to his Hog Hunter is going to be less expensive, cumulatively, than buying the rifle he really wants the HH to be. So Dr. Sandman is right ...
That said, I went thru this exercise with an old Savage FP-10 in .308 with the same blind (internal) 5-rd mag. It never really shot that well, was way too heavy to do anything with except prone-shooting, and the factory stock was crap. It did have the Accu-trigger, which I set to the lightest setting. It still shot poorly. My mid-'90s Remy PPS shot like a GAP-tuned laser by comparison.
... Eventually, after thinking of selling it, I replaced the factory crap stock with a B&C O.D. stock I found on sale. It had a much better feel, despite still having the blind mag, and the LOP was perfect. My 'smith chopped the 24" barrel down to 16" and then thinned the profile quite a bit, which also free-floated it in the B&C stock. This work took off a ton of weight, made the rifle point better as well as handier to tote in the field. When I got my SDN-6 can, we threaded the barrel to add AAC's .30 MB ratchet mount, and called it good.
I treat it now as my .308 "beater"/hog/coyote/plinker carbine and truck gun. It runs a Leupy 1.5x-5x compact scope. I don't care if it gets dropped, rained on, snowed on, pee-ed on, et al ... On the up-side, it shoots much more accurately than it did before, the SDN-6's suppression is great, and the carbine could serve passably as a quick-handling, sub-400yd SHTF precision rig.
It also means I didn't have to buy a new gun, but for what I've put into this FP-10 to get it to where it is, maybe it's a wash.