I took my 340 and 1908 1899 in .30-30 out to a range for the first time this morning. It was an uncontrolled public range, and I didn't stay long enough to set up targets because of some of the other shooters but I did shoot a box between my 1899 and my 340 before my spidey sense told me that it was a good time to go.
It was sweet shooting the old timer - recoil was almost nil, and standing open sight accuracy was OK, but I was really disappointed to find the primers poking out ~0.005 (no mic with me) and was soon kicking myself for buying a gun unfired. Then tonight I found this interesting thread about the .30-30 primer poke on a Winchester 94 site - thought you might find it interesting. I've always heard that protruding primers were a headspace issue - but this discussion points to low pressure or rough chamber as the cause with this cartridge. Don't know if that would translate to other cartridges. I couldn't feel stretch marks in any of my brass using the paper clip test.
http://www.thehighroad.org/archive/index.php/t-495803.html

By the way, the 340 is a nice little shooter!

I have had similar problems with my 1899B in 303. So, I followed the advise of a friend and shot some factory loads (I had been using low power cast bullet loads) and there was no primer protrusion at all. Dave

Sometimes there is a hard buildup in the chamber consisting of dried gun oils, fouling, etc. that needs to be removed. I used a brass brush and steel wool on a brass rod turned by an electric drill on the chamber of an M1 Carbine that was giving me problems and now it works perfectly. The chamber doesn't need to have a high polish but it should be smooth enough to let the case go backwards to re-seat the fired primer.

I never worried too much about fired primers protruding, which is a common occurrence with loads lower in pressure than factory stuff as stated above. Case head expansion/stretching is more of a concern to me in terms of safety and case life. Having the case slam back hard enough to re-seat the primer isn't a concern since I'm going to pop the rascal the rest of the way out sooner or later anyway.

If pressure signs are normal, and case life is good, and headspace isn't excessive, then go forth into the world and shoot stuff with it.

I was trying to figure out polishing the Model 99 chamber, your method gives me an idea of using a brass cleaning rod and threading a .40 cal brass brush on in the receiver, wrapping it with a bit of 0000 steel wool and using the Makita to give it a polish. It is definitely in need of it. I'm going to do a major cleaning and oiling, this will be a perfect addition. Thanks!

Oh, btw, these were factory Winchester 150 gr loads, so I'll bet the rough chamber is the culprit. It's not pitted, but it has a matte finish, so I'm betting that it's just putting a bite on the cartridge.

Yes, the Carbine chamber also had a matte finish. Putting a sheen on the chamber surface had the old girl running like a swiss watch.I also used a brass muzzle guide for the rod, just to be sure to protect the muzzle rifling. Just run the drill medium/ slow and check to see the progress. Glad that I was of help! Good shooting.