Having measured a few dozen students' Remington tactical rifles (5R, PSS, LTR) during handloading classes, this is my experience as well. Load them to mag length and be happy.Yep definitely possible.
My 700 5R Milspec .308 seats Berger 175 VLDs at 3.050 to touch the lands. Still shoots them at 1/2" typically.
don't get hung up on touching the lands. Just start at SAAMI length and work out from there.
I have a Remington LTR that shoots 100 yard bugholes with 168 SMKs/FGMM 168s and I can't reach the rifling without the bullet falling out in that thing either. Coming from a 1k benchrest/F-Class background, it really bothered me at first, but as well as it shoots, I try to put it out of my mind.Remington 30 caliber chambers have long freebore/throats. So yes. My 308 will not have any bearing surface left in the case with a 168 SMK seated to the lands. As for twist it's 1:10 unless marked differently on the barrel. It will not be slower than 1:10. It's highly likely your barrel isn't free floated in a wood stock.
2 MOA doesn't mean much without knowing number of shots and seeing the groups.
As was posted upstream, the OP's '06 is a "hunting rifle". It is designed to digest factory ammo in whatever bullet weight and design the shooter might choose. Load to mag length and be happy.
FWIW, one will usually find that bullets with a tangent ogive are more forgiving of seating length and bullet selection may help with finding best precision from a long-throated gun.