Do the rings on these cold pulls indicate there's a gap in my hot end?

Stock LulxBot Mini.

I’m having big problems with my extrusion and when I look at these cold pulls, the skirts of extra material seem to line up with the seam between the plastic and metal parts of my extruder?

First line of investigation?

It looks to be that way. You can take apart the hotend and make sure everything is tightened. If there is plastic in the threads it may help to heat the extruder while tightening. Be careful thought some of the components are very fragile.

more importantly, filament is not meant to be melting that high up, is your heatsink fan running?

Agree with @bitwolf, that looks like “heat creep” to me – typically caused by the little “5v micro blower fan” not running, or running too slowly. It’s a common failure item on that extruder (I’ve replaced mine twice). Check that the fan is running. Even if it is running, with age they can slow down or collect dirt on the vanes such that they just don’t move enough air. Pretty cheap and easy to replace if needed. Lulzbot normally carries them (not sure if they’re selling parts right now though), as does the site.

Replacing the blower fan seems to have addressed the problem. Thanks folks!