I don't get you have to spend a lot of money.
Pick up good ammo on sale as it comes up and try it out. You will find something decent. Guns all tend to be different. What works in one not so much in the other.
Frankly no one makes Match 30-06, you have to hand-load for that. I can hand load hunting loads down to 1 inch pretty easily.
308 has a plethora of rounds that are match grade. Not intended for hunting however.
If as accurate as possible hunting ammo is your need then stick with hunting ammo. If you get it down to 1.5 inches that is more than good enough for hunting.
With your setup I would say that your gun is somewhat inaccurate for whatever reasons. Remington has lousy triggers.
My brother has a 700 that requires very long and heavy bullets to shoot decently. It has a very long throat. Intended as long distance. I don't know what the SPS take is or how heavy a barrel (Heavy Barrel is usually intended for longer distances)
You have to find out what the reputation of the gun is in that regards.
The mechanical accuracy of your rifle doesn't have anything to do with your shooting skills.
You can improve your shooting skills without getting a new rifle. Take it off the sled and start shooting from field positions.
You don't seem to get that the idea is to remove the shooting skills as much as possible and try to stabilize the issue to what ammo is MOST ACCURATE taking the shooter out of the equation. At 2 to 3 inches there is some issue there.
And you don't seem to get, there is a huge amount of skill in bench rest, even doing a lead sled takes a lot of technique.
I bench shoot off bags, its my fun, try to poke 1/4 inch holes at 100 yds and let me know how it goes. Do it for 5 rounds. I usually fail.
That is my fun, for my physical condition situation (not caused by myself) that is what I can do and it too is a sport requiring a consummate degree of skill to be good at it.
In other words, there are a lot of shooting skills as well as techniques.
Each to his or her own.
