I'm totally confused...I just miked my 7.62x39 SKS ammo at 0.308" and my Moisan Nagant 7.62x54 Russian Rimmed at 0.311" and now Spanky stated the two have the same bullet diameter...someone or something it totally wrong...

...I don't know for certain what the bore size is in the NEF for the 7,65x39...
While you could shoot the larger diameter bullets in the smaller diameter barrel...it has been done many times in the past...it increases the pressures substantially...causes more wear and tear on the weapon...and generally isn't as accurate...going the other way, the smaller bullet in the larger bore just makes for lousy accuracy and a quickly worn out throat. Both alternatives are not good.

If you somehow have a barrel with 0.311" bore...slug it to be sure...and wanted to waste some money, I would rechamber to 303 Brit and be happy...ammo is available, but not as cheap as the x39...
What you could do to the 7.62x39...if the bore is actually 0.308"...is rechamber to almost any(within reason) 0.308 cal cartridge...BUT...why do it...you can have NEF put on a new barrel cheaper than having the old one messed with.
As far as I'm concerned there is nothing wrong with the 7.62x39...it has plenty of pizzazz for up to deer sized animals withing reasonable distances...plenty of cheap "hosing" ammo available...why change a good thing...what's not to like.

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If you want something with more muscle...get a barrel in a larger caliber/case...a much cheaper and reasonable alternative. The x54 Russian has about the same ballistics as the 307W/308W/303 Brit so why not just buy a cheap Moisan and be done with it...it might be cheaper than doing a rechamber and you will have another rifle to boot.

It costs me $50-55 to do a rechamber for the reamer rental alone and the few local 'smiths charge $75-150 to do a rechamber depending on the setup time, if they have a reamer and how critical the headspace is.
There is also the 7.65 Mauser, 7.65 x 53 and 54 "Argentine" that are similar is size and ballistics, but also 0.308" and 0.311-0.313" bore sizes and that can get real confusing when being discussed.
Luck on your projects.