After tightening the screws on the X-axis gantry and doing the bed leveling and test prints again it seems to have gotten better.
Also, while I was under the impression that the V2's heated glass bed _should_ work well without adhesive, I applied a bit of glue stick and now my first print seems to have a perfect first layer.
I may just have been confused because I needed to turn the Z-offset way down to get it to stick in the first place, and then tweaked it upwards to get nice lines, meaning I would have to dial it back down on next test print and so forth.