Why are you tumbling twice? That's not necessary. Even if the brass went in the mud, you can just rinse it off.
Just neck-sizing for a bolt-action should always be fine. After firing, the brass will be fire-formed to the chamber. You are re-sizing the neck because after firing the neck has expanded too much to grasp the new bullet when you reload; it was fire-formed to that rifle's chamber neck too. Even many semi-autos will fire their own fire-formed brass just fine after neck-sizing, without any sticking problems. You DO have to make sure that fire-formed case hasn't grown longer than the SAAMI specs though. After you fired that last round, you say the case was stuck in the chamber. If you fired it, it would have just fire-formed itself again to that rifle's chamber and should not have presented any difficulty in extraction. The only difficulty should (possibly) have been in chambering the cartridge prior to firing, not after firing. I only own one .308 semi (SCAR 17) and often just neck-size my brass (it lasts a VERY long time that way). No issues chambering or firing or reloading cases repeatedly. Same with an old (Armalite-made) AR-180. I've only bothered to neck-size for that rifle since I bought it in 1970 or 71 (used to use a Lee loader and a mallet for that). Never given any problems, just needed to trim the length and anneal those necks every 5-8 times fired or toss them when the neck cracks. You can not just neck-size brass that was fire-formed in ANOTHER rifle though. Certainly not for any semi that I have ever encountered. But you DO have to trim those cases to correct length, and although it happens slowly, the cases will gradually get longer and longer until they are too long, so you need to always check case length and trim them back to spec. If you have stuck cases after firing, the problem isn't the neck-sizing. Especially after the case has cooled and shrunk. It is something else. If it is a semi, then I would expect an extractor failure. On a bolt-action, I would expect some chamber issue, or a serious pressure problem with the reload, but not even that after the chamber and cartridge cooled down (10 minutes max). Don't know what kind of action you are using or what caliber so difficult to say more with any accuracy. Unless you want your brass shiny-new, why are you bothering to tumble it even once. If it's a semi, get a brass catcher for the range and just tumble occasionally when it doesn't just wipe clean I do that after annealing (sometimes). You gotta trim it to length though no matter what yo are doing, but that should only cause a failure to chamber, not a failure to extract. You should consider a lube that doesn't need to be removed before reloading. many wax based lubes won't mess with your powder, and I only wipe the outside of the case so they don't attract grit. But I don't usually process and reload more than 50 or 100 at a time.