As you are reloading already, you are going to be limited in what you can do.
More accuracy will come from a new barrel vs a new stock.
However, there are a lot of economical stocks that can be had in wood laminate if you will do the final finish. I just used a Bruce Baer sporter that he can send inletted and pillar bedded to you for final finish. www.baercustomrifles.com
look under sporters. the thumbhole has a 1 3/4" flat and is super nice handling with magnum calibers in particular. My gun finished at 9.2 lbs with 26" barrel, stock, sling and scope. He makes them in solid wood and any color laminate. I used a light color super light butternut that finished 2.5 lbs bedded with recoil pad.
Midway normally has decent deals on shilen blanks in stock. Lilja normally lists his overruns for immediated deliver on his site (I just got a #4 delivered in 4 days for $300 shipped. Chamber, rcvr faced, lugs lapped and new recoil lug will run $200-275 normally.
Nothing wrong with the factory trigger for hunting gun.
I would save money and buy the barrel, then stock and have all done at once otherwise it will cost more money to rebed the rifle etc.