Hey Art G!
I've owned three Rem m788's through the years and they are generally good rifles. The first, a .30/30 was an honest 1/2" 3-shot group rifle with certain loads (ONE HOLE GROUPS!), the best being a Speer 130gr HP over 30-something grains of IMR4320. It took a bit of tweaking the stock and trigger to accomplish though. The second was a .243 that was good for ~3/4" to 1" 5-shot groups (@100yds) out of the box favoring 80gr Hornady Spts and H4895. The last was a slightly more problematic late production .223. It was very particular about bullet/powder combinations and seating depths, but when cool with a lightly fouled bore, was occasionally good for 1/2" 5-shot groups.
Good rifles for the money, my .30/30 cost me $69.95 plus tax in 1971, while I was a freshman in highschool
However, they weren't perfect.
There are several possibilities with your rifle;
#1. The bedding issue that you mentioned. I would try taking a 1/2" or 3/4" sanding drum and removing the "hump" on the stock near the forend in the barrel channel. Then, I would glass bed the action around the rear tang guard screw (rear action screw), the front action screw and the first 1.5-2.0" of barrel shank. If this dosen't work, then install a "Bug-hole barrel tuner" (a counter sunk set-screw in a threaded stud that can be progressively tightened to adjust forward barrel pressure- particularily suited to tuning to a specific load, or on rimfire rifles).
#2. You may have a "rough" barrel. In which case you have two alternatives: Lap the barrel you have (either hand or "fire" lapping), or, replace the barrel, which of course may affect the collector value of your rifle. (This would not likely cause the group walking, and then "settling" down you related however.)
3. You have a barrel that is/was "crooked" to begin with and is warping as It heats up. Back in the '60's and early '70's when your rifle was likely made, it was common practice for the barrels to be straightened after drilling/rifling and being heat treated/stress relieved if they weren't straight. Not neccessarily bad barrels, but just "curled" after being drilled and rifled and then heated to relieve "stress risers" that are induced from the cutting processes.
I had a Rem m700 ADL my senior high school year that suffered from this. By waiting 10min between shots it would shoot 3/4" to 7/8" 3-shot groups with a Sierra 168gr BTHP. I won a third year-straight regional science fair contest with my testing, refinements and conclusions with this rifle/project. (Previous years were different projects and subjects, but this was my favorite one, obviously! One of the judges particularily liked my testing of different primers and corresponded with me several times before I went to college- He was a shooter too!)
The only fixes I know of for #3 is either try Cyrogenic treatment of the barrel/action, or again, rebarreling. However, there is a possible but remote possiblility that cutting the barrel down (assuming it's a 22" bbl) and recrowning just might take away any problem areas of the barrel, and has the effect of "stiffening" the barrel too, changing its harmonics.
Also try this FIRST!
Most shots hunting (especially with a .308!) are the first shot, from a cold barrel. Try firing your shots with at least 10min. intervals and see if it groups. I have a Marlin .30/30 that is like this. Second shots are not an issue as:
1) Most shots are close- less than 100yds on deer, and;
2) a second shot if needed, is not critical for accuracy anyway as deer is probably moving, or is a second deer, of course!---- more likely than a deer needing a second shot in my experience)
If not, then try steps #1-3, in that order leaving barrel replacement for very last resort.
Good luck!
