As described in a guide on DownSights, it turns out that the key to unlocking those weapon attachments and earning the 150,000 XP needed per weapon at nearly double the usual rate is to play Zombies - at least this will give players a reason to do so, as the content-bare and half-baked Zombies mode is one of the major points of contention with the game.
That said, this method doesn’t task you with playing Zombies properly, as that would likely be time consuming to a degree comparable with regular play. Instead you need to score just 35 kills against regular zombies, quit the match and start again. Go to 35 again, rinse and repeat. What’s more, you should be using melee attacks, which inexplicably yield more weapon XP. The way the game mode pays out XP results in diminishing returns after you blaze through those first 35 kills and the amount of time you invest beyond that offers comparatively poor rewards. Apparently the best approach is to jump into a solo match of Der Anfang, melee all the basic zombies around the initial spawnpoint, then beeline it to the closest Harvest portal where you’ll be facing plenty of similarly weak enemies straight away. Bash heads until you’ve killed 35 enemies and quit. While this relative shortcut to 150,000 XP does speed up the process, you’re still looking at a long grind of punching zombies to death to unlock those weapon attachments. This method is easy but repetitive and tedious, so be prepared for that if you’re adamant about grinding out weapon levels fast.