Thanks everyone. Continued thanks for all the feedback and comments. If the right person is someone who has all the answers then I'm not the right person I guess. But, I'm not an incapable person either.

If there's no safe way to do this, then I'm totally ok skipping the lights. But what would you guys do? Code-compliant or nothing? Or wire to the outlet?

To answer DerbyDad03's concerns:

[DD03] One of my concerns is that if we just tell you to drill a hole in the wall and fish that cord into the receptacle box and use wire nuts to match the
wires colors by color, are you going to be able to do that safely?
[C13] Yes, I can confidently do that. I tested it it "outside" the wall to check functionality and overall lighting effect of the LED panel.

[DD03] Will you know if the box is so over crowded that you are so out of code that it is now unsafe?
[C13] I don't know. I'd have to look it up. Any advice here?

[DD03] Do you know how to safely attach stranded wire to solid wire?
[C13] Yes, I've done that before. Wire nuts, plus add a bit extra length to the stranded wire? Or wrap some stranded wire around the solid wire before the nut?

[DD03] Do you know how to safely secure the wire to the box? (You might recall from my previous posts that I'm not even sure that it is code (or even safe) to
run that cord inside a wall and into a junction box.
[C13] I'd have to look this up too to check. I was going to copy the securing nut/grommet I see on other boxes.