Okay, so the problem didn’t recur on the first PLA print I made. I used the exact same print file, changed nothing aside from the filament type, and it printed flawlessly. I thought maybe it was something with the PETG specifically that would be a cause (possibly?) but I had no idea what it would be aside from a defect causing a feed issue that it was trying to compensate for, and it somehow threw things off. Turns out that isn’t the case.
I did additional prints, PLA again, and the first one ran just fine but the repeat of the exact same print placed the first layer at the correct spot and then offset the rest of the print by around that same 3mm+/- offset again. Every bit of it aside from the first layer was offset up and to the left.
I’m beginning to wonder if there’s not an issue with the servo(s) that’s causing slippage under load at high move speeds or something, or possibly a belt skipping on the gear(s) during fast movements.
I’m going to run through every conceivable calibration and setup I possibly can on this thing and see if it makes a difference, because at this point it’s looking like a mechanical issue and nothing to do with any specific filament type or profile.
And something I didn’t mention in the initial description: I’m seeing some use of the term “Vision Encoder Plate” and don’t know enough about 3D printers in general to know exactly what that is, so I’m gonna go to Google university for a bit and read up on it; however, if anyone has a quick cliffnotes version that would be appreciated 
Further, just for additional info that may be relevant (no idea), I’m using the textured PEI plate 
I appreciate the input I’ve gotten so far, and I’m going to be trying to pull the timelapse of the last print and seeing about putting it in here for your viewing. Only reason it’s not being added to this comment (novel) is because this printer is a work device and we have a separate standalone laptop that we run it on that does not have a corporate image on the main drive, so going between the corporate and non-corporate devices with a thumb drive is prohibited due to data security policies, and I have a bunch of hoops to go through to be able to do that.
EDIT: Reread your comment and realized I didn’t answer some questions even though I’ve rambled enough to require an editor and a publisher. Both of the prints where this issue has occurred have been very close to the edge of the plate. The second PLA print isn’t a single large print file though; it’s 6 separate ones (they’re just small drink coasters) stacked in a 2x by 3y configuration then centered via the slicer’s center function. I have asked if we ordered the vision encoder plate with the initial printer order to see if we can run that calibration also, but nobody will be back until Monday or Tuesday that can answer the inquiry.