So, I was able to fix this (or it fixed itself overnight as these things sometimes do) with a 5°C increase in extruder temperature to 210°C. The Sunlu PLA filament specifies 200°C - 230°C as its print range.
I followed the advice of a IRL friend who suggested "What happens if you raise the z a bit so you can see the nozzle and keep raising the heat until it starts to come out on its own. Check temp and then run a print at that temp."
I only needed that 5°C increase before I could see it oozing. From there I was able to successfully print a calibration cube and further model.