I have a Savage LRPV in right bolt, left eject, with a Target AccuTrigger action. It has some pros and cons. I got it in a 12 twist 6BR. I thought it would be chambered with a throat suitable for a 12 twist, but it is not. The throat is long and 68 grain flat base bullets are the lightest I can shoot, and even then I believe the long throat causes issues. If you buy a 7 twist .223 F/TR model, you would hope they would put a long throat in it for the long/heavy bullets, but you might want to check with the factory before you lay your money down. I shoot off the bench with it, and the HS Precision stock is well made with an aluminum bedding block, which I further bedded, but the shape of the stock is poor for shooting off the bench. I would much prefer the 12 F Class stock with the flat rear and 3" wide flat front. But, I guess you have to comply with standards for F/TR, if that is what you plan to do.
On the positives, I was able to set the AccuTrigger down to 6 oz. It does have a bit of a quirk that you need to be sure the safety is full off before you try to shoot. Accuracy at 100 meters is very good, despite the long throat. I tend to get a flyer every 10 shots or so, and I attribute it to the throat. Here is three consecutive three shot targets where I managed to dodge the flyer.
On your option to buy a Savage action and add the barrel and stock, I would spring for the extra cost to get a cut rifled barrel over a button rifled. Building your own, I believe gives you the option of the right bolt, left port, which I find very handy. But perhaps there are rules against that in F/TR...
Just my thoughts!