In that case it may be the filament. Unbranded and from a crappy printer manufacturer? That’s not a good sign.
I’ve gotten 95% of the issue resolved. First of all, I replaced my Marlin firmware with straight up Repetier. Second, the filament jumping out of the drive I believe is due to skewing in the roller bracket (see photo). I’ve temporarily shimmed it to counteract and it helps immensely. The bearing is not slotted, so rectifying that will be the next step.
Thanks to everyone for the advice!
missing/deleted image from Google+