The kids like it, it is sentimental. As mentioned before, I would have a Smith check it out.
One thing I have not heard mentioned, but I have seen a lot at the range... You are supporting the rifle on sandbags, with the front of the stock on the sandbag, not the barrel? I only ask, because I see it all the time at the range, and people wind up with odd "groups" because of it.
On the range, I always support the rifle on sandbags, under the fore-stock, and under the rear of the stalk.
I reloaded for a Rem 700 30-06 a few years back. Speer 150gr spire points in Remington brass, with 4064. I had to take my time with the sporter weight barrel, but it would group 1.5" or a little smaller all day long.
I have been shooting some 30-06 Ackley Improved in a Win 70; I notice more creep with it. Definitely more sensitive to the barrel warming up. But I don't have to wait more than a few minutes between shots. Certainly not 20 minutes.
You've covered most everything already...
- possible pressure point issue at end of stock
- torque of screws retaining action in stock.
- Scope and mounts removed, degreased and cleaned spotless before assembly
- base installed spotless clean, with screws blue lock tight
- rings installed spotless clean, use a dowel to ensure alignment before installing scope
- scope spotless clean, rings and screws spotless clean, and installed
- Barrel kept clean, copper fouling removed
Those are the things I have seen that would affect accuracy and repeatability.
Before this most recent shooting session the gun was completely disassembled and cleaned. Scope removed. Base removed. Rings removed. Bore cleaned thoroughly with bore cleaner. Gun re-assembled, put in different stock (well tightended), Millet base put back on (blue loctite on screws) and tightended thoroughly. New scope put on. Bore sighted. Three shots at 25 yards in a 1 inch-ish group, a little high. Cools for 20 minutes. Next two shots at 100 yards are centered, 8" high and about an inch apart. Adjust scope downward. Wait 10 minutes to cool....barrel cool to touch. Shot labeled # 3 on image posted is the next shot. Dead center bull's eye and exactly where the adjustment should have placed it. Let barrel cool again. Shot #4 is high. Let it cool for at least 20 minutes, no adjustment and shot #5 is the result.....almost touching shot #4.