Update for anyone who cares...
So I mounted the action in the Hogue pillar-bedded stock, and headed off to the range. I had a couple boxes of handloads to test for various things, but the first test I wanted to run was group size for free floated vs. upward barrel pressure. I first shot some handloads I'd gotten decent groups with (under 2") from the free floated barrel. Then I allowed the barrel to cool completely, and shimmed under the forend tip with one layer of neoprene, cut from an old set of waders. Three more shots, and no real change. But that single layer just took up the space between the stock and barrel, so I added a second layer so there would be positive upward presure, and allowed the barrel to completely cool again.
That's when the magic happened. The next group was 0.5" ! All three holes were nearly touching! I was shocked but thrilled at the same time.
So I left the double layer of neoprene in place and ran through all the rest of my reloads, testing different charges of RL-15 and different bullet seating depths. Twice I hit a magic combination. First, with the original loading (38 grains RL-15 under a 140-grain Sierra Game King at 2.925" OAL) and again with a similar charge and OAL under the 162-grain Hornady SST.
Between the up pressure on the barrel and the precise OAL, I had finally found something that worked.
Only, I was not in love with the Hogue stock. Just too darn heavy, and the barrel channel was too wide for that pencil-thin RSI barrel.
So I thought "what would happen if I put upward pressure using the neoprene shims in the factory full-length walnut stock?" I had to at least try it.
I removed the Hogue stock and got out the beautiful full-length walnut stock. I had previously free floated the barrel in that stock with a combination of reliving the end cap and the barrel channel, and shimming under the front of the action with aluminum shims. To get the upward pressure I wanted, I again put two layers of neoprene under the barrel at the end cap, removed half of the shims under the front of the action, then I tightened down the front action screw as hard as I could by hand. After tightening the other two action screws (rear screw tight minus 1/4 turn and center screw just barely snug), I went back to the front action screw, got out my cordless drill and flat bit, and set the torque to the max setting. I then torqued the hell out of that front action screw, to the limit of my Dewalt drill's ability. I have no idea what that is, but I wouldn't be surprised if it was 100 in. lbs. or more.
I then got my exacto knife and carefully trimmed the two layers of neoprene just below the metal end cap so you can't see them. You would have to look very, very carefully to even know that neoprene is under the tip of the barrel now.
Then I shot a 3-shot group (no waiting) with my best performing load at 100 yards. Bingo! 1" exactly and the last two shots were touching. I made a tiny adjustment in the scope and moved back to my zero-distance of 140 yards, and shot two more without letting the barrel cool completely. Both shots were inside a 2" x 2" square, about 1" apart. Perfect!
Now I will try this same load over the course of a few days to see if I can detect any changes in the POI due to that wood stock.
After a great deal of work, I finally feel like I'm getting somewhere. I can understand 100% if someone bought one of these beautiful RSI's and decided they weren't worth the effort required to get them to shoot halfway decent. I nearly came to that conclusion several times myself in fact. But I didn't want to give up on this gun, and figured I may even learn something in the process. I think I have. If it continues to shoot as well as it did today, I'm going to be thrilled with my decision to buy it.