The cases "sticking" to the chamber walls isnt bad, thats exactly what the case is supposed to do, and one of the reasons for some Ackley modifications. Your chamber may be a bit rough if its marking cases, but I don't see it as a problem unless it's actually damaging them.
I'm curious as to what your gunsmith says. You no doubt noticed the post above where natman tried the headspace gauge, and it was in spec? If your guy says it's in spec, but wants to go to heroic measures to "correct" it, I'd ask if the work is free if the primers still back out afterward. What I'm saying is, this is a misunderstood thing to many, and, as natman and others have indicated, the gun can be in spec and still back primers out some. It simply isnt a disatrous problem as some seem to feel. 30-30 cases are thinner than most rifle cases, the cases adhere to the chamber walls rather well at the lower chamber pressure of the round. There
has to be some headspace clearance (which is exactly what "headspace" is, the required space for the cartridge to chamber properly, and within set specs) for the cartridge to chamber, and to allow for variances in difference cases. You can polish the chamber and make the primer thing go away, but you are also causing more bolt thrust. It isnt likely to cause a problem, but that's just what the result is. You can oil the case and get the same result, but that isnt recomended. Ackley did it to make a point. The primers reseated, but the cases function properly when they adhere to the chamber wall enough to contain the pressure, but not stick when extracting.
To put it another way, the very fact that the cases are adhering to the chamber wall, and the primer is backing out a little, means the case is functioning properly. That there's is a small amount of room for it (the primer) to move isnt a problem, it can be within headspace specs and still do this.
FWIW, Winchester used to make various sizes of locking bolts. I have examples in +.005", .010", and I believe .15" oversize. They are marked on the bolts. I've picked them up at gun shows from parts guys, usually paying $10 to $15 each for them. After the little adventure with building up the rear of the bolt on the one rifle, I quit worrying about it. I figured that if I had a rifle that had more than average primer protrusion, and showed true excessive headspace clearance, I'd deal with it with one of the oversize locking bolts. Until then, I'm not worrying about the small amount of protrusion that about half of my 94's show. If your guy says that your gun is within spec, or even if its out, you may want to try finding an oversize locking bolt. This is something you can do yourself if you know how much room you need to deal with.
Here's a pic of oversize locking bolts.
"...I'd hate to lose this externally pristine example, but my confidence in the gun is shaken, and I'm not clear I could ever get over the concern every time I tickled the trigger, unless it can be fixed.... I'm obviously not mentally built like you Malamute!"
No reason to "lose" it. If the gun is within spec, enjoy it. I carry a couple of mine walking along the edge of the mountains. There's large, sharp edged critters there (Grizzlies and Mt Lions). A 30-30 isnt a bear gun, but I have absolutely no qualms about the reliability or safety of my Winchesters.
This was an absolutley thrashed 1927 carbine. I cleaned it up, it looked like it hadnt been cleaned in any way in 50 years of hard use, and have used it regularly since. It's the one that I built up the bolt on to minumum clearance to be able to close on a case, only to still have the primers back out a little. It functions perfectly.
Another misunderstood thing about Winchesters. If, or when they have problems, they don't "blow up" like bolt guns have at times when they have catastrophic problems. So far as I know, when Winchesters "let go" its always been a barrel that goes,
not the action. I've never heard of, or seen a pic of an action that let go. The receiver may be damaged, but it's the barrel that starts the festivities (similar to the fact that revolvers cylinders let go long before a frame does, if the frame went, it was started by the cylinder). The bolt doesn't come back in your face, as some assume. One guy rebarreled various lever actions to 454 Cassull to see what they would take. Of the several Winchester 94's and a Marlin 336, he tried, none "blew up", tho they did stretch the action to the point of being unsuable, as in, simply wouldnt function. This happened in from 20 to 50 rounds of 454 Cassull. If anyones interested, the Marlin 336 failed sooner the Winchester 94's did. The Marlin receiver walls bulged outwards from the locking bolt trying to move backwards. The Winchesters stretched the sidewalls of the receiver visibly, particularly the angle eject gun tried. Either will last a lifetime of hard use when used with the standard rounds the guns were made in, even with some slop in the action. If anything happens to them other than a catastrophic barrel failure, they will simply get so loose they stop functioning. I've never seen one that loose in the many hundreds of 94's I've seen.