I've been using the 260 SAAMI chamber for nearly two decades. It's looser, but can be dealt with via an old, traditional BR handloading technique; called partial length neck resizing. It was an earlier effort to manage neck tension prior to the arrivial of neck bushing resizing dies.
It starts with 7mm-08 brass. The 260 Rem F/L resizing die is adjusted to only resize the forward half (or so) length of the 7mm-08 case neck. The aft, unsized portion will usually chamber easily, while the forward, sized portion does the bullet retention task. There may be a concentricity bonus going on as well. The result is a sorta hybrid 7mm-08/260 Rem case.
Some advantages:
The case neck sits centered in the chamber neck, and also seals better. Carbon staining stops abruptly at the length where the neck diameter flares. Case cleaning consist of a firm wipe of the neck area with an alcohol dampened shop rag.
Incidentally, my case lube is the RCBS water soluble product, applied by spinning the cases manually with one hand while pinching the neck in the fingers of the other hand, moistened with the case lube. Lube removal is simply a repeat of the neck wipe with the alcohol moistened shop rag.
The shorter neck/bullet bearing length results in reduced neck tension as well as less neck length where work hardening occurs.
The raising of the F/L die results in the unsized portion of the lower case wall remaining expanded, reducing work hardening in this area, as well as ensuring a snug fit where that portion sits in the chamber, possibly centering the case base better. This, combined with the neck centering, allows the case to be both centered and aligned with the bore axis. The intent is to gain some concentricity advantage without the usual rigamarole.
The whole operation allows the F/L die to do a better job.
Other issues:
These cases are going to need a shoulder bump occasionally, and the die adjustment prevents that.
I have a way to address this, too. From the shoulder down, the 260 case should be identical with the 308 case.
I also shoot .308, and I use the physically same case gauge and headspace gauge in both my 260 and 308 headspacing (Savage rifles) and handloading operations. Everything is based off the same identical set of dimensions.
So, by removing the decapper stem from the 308 die, it becomes a good bump die for the 260, and the .260 die adjustment can be left undisturbed (Dillon RL550b press). My 308 rifle setups involve semi's and the partial length resizing setup is not used for that chambering.
This PL resizing scheme was initially intended by me as a variable approach to managing neck tension. It does that, but does not address work hardening. I'm not going to do annealing, so this part of the theory remains unexploited.
I do not employ custom chambers, and all of my chambers are cut to SAAMI spec. Tricks like this may allow one to eke out a bit of accuracy improvement from the SAAMI chamber.
Greg