I took a 6 year hiatus from this game, and as such had to redownload it to complete all the achievements. And even though I had 34 non-DLC stars in Spec Ops and the Unstoppable achievement, it kept my leaderboard stats and cleared my Spec Ops level.
Finishing all of the on-disc (solo) missions on Veteran, two rounds of Chaos mode, and all the DLC missions on Veteran plus the associated achievements got me back to level 37. Which is to say, less than halfway through the XP required to get to level 50.
So, there are two options here. Either way, it's a good old fashioned RPG-style (not that kind of RPG) XP grind. The fastest methods are:
1) playing the first minute of Server Crash, which can be done solo on Regular and net 4000-8000 XP per minute, roughly.
2) you can play the first minute of Fire Mission either co-op or with a second controller that is AFK. This method, when done properly can net about 8000-11,000 XP per minute. Mixing things up between these two missions, and taking breaks to go and get the newly unlocked items from the Survival Armory can break up the repetition. I also recommend watching a podcast or livestream while doing this.
Much faster, but beware that while this is the fastest way to level up, when you get up around level 40, you're still looking at 50,000 to 100,000 XP per subsequent level, with each getting progressively more far-reaching. Total XP for level 50 is just over 2,000,000.
Tedious, but not impossible, and as someone who had to grind for 100,000 Nuka-Cade tickets twice in Fallout 4 (thanks XB1 for no offline achievements), this was by comparison much easier.
Be sure to keep a physical list of all the items you have bought. The list can be found in other solutions. Also remember, very important, that you must buy one item, exit the armory completely, and THEN buy the next, or it won't count all but the last one bought. You only need to buy every weapon once, and each attachment once (not once per gun). The grenade launchers are specific to their respective weapons (M203-M4A1, GP25-AK47, M320-ACR 6.8).
Lastly, DON'T FORGET TO BUY THE FIVE SEVEN
I should have just done the work to make a physical list back in 2011 and get this while I was still level 50. But oh well, happy hunting.