Model14
Since you asked this on the Bencrest Centerfire Forum, I will give you an answer that is brutally honest.
Your statement "improve my group aggs, (get it into the twos)", is totally unrealistic. I feel safe in saying that there is no Factory Barreled Remington 700 on the planet that would poccess that level of precision. Sure, you might accidentally shoot a "two", but agging that is an entirelty different thing.
You did not say what chambering you have. But that has a lot to do with the overall accuracy capability of a Factory set-up.
If it is a 223 or a 308, I would say that you could realisically look at achieving .400 accuracy on a regular basis.
That takes a lot of load development, the best in bullets, the best in bench equipment, plus a good set of wind flags.
Of course, any Rifle will shoot better when you do find what that ideal seating depth is. Your theory that the bullet and shoulder will hold the round true holds water untill you realize that Factory chambers are in no way "true" when speaking in terms of precision barrel work.
Most Benchrest set-ups shoot at their best when the bullets are touching the lands, or into the lands some. Most Factory Remington Chambers won't even allow a shooter to get there because of the long free bores. That is, unless you are using rather long bullets for the caliber.
The best thing to do is take your loading equipment to the range, set up a good set of flags, and start going in or out with the depth untill something shows promise. Then, shoot at least three 5-shot groups with that setting.
Remember, to achieve the kind of accuracy that you are looking for, you are wasting your time unless you are using wind flags.
To give you an idea how 'agging in the twos' looks, at the recent World Benchrest Championships, the vast majority of the shooters were no where near 'agging in the twos'. In fact, when looking at both Grand Aggregates, only seven shooters stayed under .300.
Sobering, huh.......jackie