Aside from the initial this has all been on the textured sheet and has all been PETG. I've been experimenting more, setting my bed to a lower temperature, which seems counterintuitive but seems to be having positive effects.

I'd normally print a test layer out of solidarity, but unfortunately, my Mk3 is out of action awaiting parts. I did have a bad experience with a textured sheet, so would try PETG on the smooth PEI (with a spritz of Windex) to test. Other than that, it sounds like you're making progress. PETG should stick firmly for your 1st layer just like PLA, so the same basic procedures apply. Good luck with it!

It is possible to get a bad textured sheet. I had one that was a complete write-off. You can print PETG just fine on the smooth PEI, but be sure to put some sort of separator agent (Windex is recommended) before printing higher temps on it. 

Yet this is still a failure... Same Z-Axis, same temperatures and layer height as the square.

I read through your site and I really appreciate it, seems real clear and I think I'm moving in the right direction. Here's the Z-Height that I had in my original post, which is what I'd set using the original method -1.350, for the entire thing.

Those pics look very close. You can try going a bit lower to see if the little dots along the edges close up. When you peel it off, it should be a solid sheet.

I do tend to prefer the textured sheet and have been using it for PETG, but my original post I was just trying a bunch of different things to try to get it to work. I haven't scrubbed it with Dawn though, is that potentially enough to cause what I was seeing with the original hexagonal shapes? 

Possibly. If your bed adhesion isn't good, parts tend to lift easily which can cause the nozzle to snag.

Mastering the PEI takes a bit, but it's worth it not to have to use goop on your bed, brims, or (shudder) rafts.

Some slight gaps in the top left there. 

I do tend to prefer the textured sheet and have been using it for PETG, but my original post I was just trying a bunch of different things to try to get it to work. I haven't scrubbed it with Dawn though, is that potentially enough to cause what I was seeing with the original hexagonal shapes? 

• If the angled lines have gaps between them and there are gaps between the angled extrusions and perimeters, you're a bit high. Move down (make more negative) your Live-Z by 0.04-0.06mm gaps until they start closing up, then lower by 0.02mm until it looks even.
• If the angled lines are rough, the nozzle is probably dragging. Raise your Live-Z (make less negative) by 0.06mm and increase by 0.02mm until it smooths out.

You're better off starting a bit high (the gaps are easy to spot) and move down as the gaps are easy to spot.

If you have no luck, take your PEI sheet to the kitchen sink and use some Dawn dish soap (or equivalent) on it. Nothing with hand softeners. Scrub it with a plain paper towel under hot water, rinse it, and dry it with another plain paper towel. Dry it but do not touch the print area. Don't do anything else and try Live-Z adjustment again.

If you are printing PLA, use the SMOOTH PEI sheet. If printing PETG, use the textured PEI sheet. Be aware that each has very different Live-Z requirements due to varying thickness.

Starting with where I left the grid it was a complete failure, -0.8

So I decreased the Z-Height to -0.9

And then -1

And it feels like it's trending in the right direction. However, this is further than was required in the square so I'm not sure if I'm doing something wrong there or not understanding what you mean by having it at the "just starting to stick" point.