I've built several left hand remage rifles with Remington actions. You can find old left hand 700s for $500 and criterium barrel and barrel nut for $500.
I just put a Pierce action on a 6.5 creedmoor criterium heavy sporter in a Pure Precision stock. I have just under $2500 into it and got to tell you its worth every penny. While my Remington actions builds shoot pretty good they required load development, bedding, on and on and on. The Pierce action fit like a glove in the Pure Precision stock, adjusted the head space torqued it to "guten tight" and shot it. Its by far the best shooting rifle I've ever owned. Custom actions great but the wait time is painful.