I see a lot of posts here saying that the books are just a guide - that maximum listed loads can be exceeded as long as there is no over-pressure signs in YOUR gun.

Here may be a case that points in the other direction and very few are seeing it. This rifle is apparently having over pressure signs (if the chambers are polished) and the shooter doesn't want to admit that in THIS gun he needs to reduce pressures by backing off his load.

Reminds me of the saying, "if it doesn't fit, force it. If it breaks, it needed to be replaced anyway."

Sticking cases is a symptom of a chamber problem. Either the chamber is rough or the pressures are too high in that application.

Pauls,
I prefer a lapped finish rather than a polished finish to my chambers. I have seen chambers that had rings from reamer swarf that made extraction a little rough though.

The Rem 700 is a tried and true gun, that has been around for a long time, with that being said, I think that you need to first look at what your ramming down its throat. Is it over powered- too much, to many grains? I suggest that you reduce your loads(grains) down by 10% to start with and then shoot and see if they still stick. If they still do, then take it to a good gunsmith you trust and explain the problem/situation, your having and have him look with a bore scope and see if there is any rough spots in the bore that are grabbing the case and not wanting to let go. Maybe a polish will help your situation out.

No matter, you need to get it taken care of now and stop using it, until you do, because if not, then you might have a castistrophic incident at the range, where either yourself or someone else will get hurt, then that changes the whole story into something else!!!

If there are rough spots in the chamber, they will show up on the brass, so will rings or other faults.
The best thing to do if the chamber is rough, is drill and tap the primer pocket of a FIRED case to 1/4", a case remover kit is set up for this, thread this onto a 1/4" rod, coat with mild polishing compound, Autosol liquid polish works really well, and polish the chamber, then to FINISH the job, use some scotch brite pad and spin a few seconds to give some roughness back to the chamber. I normally put the scrotch brite through a cleaning rod loop and do it by hand in my lathe, but a hand held drill should work for both methods.
If this doesn't work, your extractor may be damaged, does the rim get torn off when the cases fail to extract?

Cheers.

I replace more Savage extractors in a year than Remington 700 extractors by a 3-1 margin. Most often the Savage gets a little dirt in the spring and the extractor and the ball and just fall out.