Order all the SMD LEDs you can find for next-day delivery on Jolly Jeff's Shenzhen Express. Not enough? Find another seller. Who cares if they don't match? Also get the first set of usb sockets that'll arrive. Get some 18awg wire (it's under 1mm) and some 24awg wire (This can sit on the pads and still be under 1mm). Also get some high-temp double-sided tape. It's not hot enough to survive much direct iron contact but YOLO so just send it and see what happens.

This step is mandatory.

You need a low-level QR library like https://www.nayuki.io/page/qr-code-generator-library so you can modify the code until it works. Turn error correction all the way down, and then keep changing your URL until it the qr is the minimum size possible. Change the mask pattern until there's no large blocks of light or dark pixels.
Now's the fun part: Count the pixels and make sure you have enough LEDs. There should be less than 250, with some allowance for losing them or burning them out.
Print out a dozen copes of  your QR code until it is sized like a business card and each pixel is roughly the size of a 1206 led.

Arrange all your double sided tape in the shape of a business card.

Steal some tiny tweezers from someone else in your house so you don't get your nice ones bent up. The best way to do this is peel the tape back a tiny bit, stick your qr to it, and start placing one row at a time next to the paper.

Hand-placing each column means you'll have skew between the rows and that'll mess up timing on the qr. Hard for software to compensate. You should have known better. Try aligning them with a hackaday ruler.

Realize you don't want to manually align every row, and it would suck despite the work you put in.

Get the weakest clear double sided tape (or 1# picture hangers in my case) you can find. Print a mirrored copy of your QR code and stick it to one side of the tape. Remove the protective bit on the other side and throw your tape on the ground. Then touch it all over your fingers. You want it as minimally-sticky as possible for later. You could probably lick it too. Put your LEDs upside down on the other side. This sucks way less than the other way, and is more accurate to boot. Look at the symbol on the bottom and make sure they are aligned properly. LEDs should be aligned in alternating rows (check anode and cathode). Make sure to mix your miscolored LEDs into the big blocks so they blend in.

Make another array of high-temp tape and put your LED-QR on it, LEDs facing down.
If you ruined the sticktivity of your clear tape enough the LEDs should stick right to your good tape. Peel back slowly and you won't have a single LED fail to transfer. This worked perfectly first try for me, so it will for you too. The rest of the project is sure to go this smooth, too. You're less than an hour from being done, now.

Cut a couple of pieces of 18awg for the frame/main bus bars, then you need to cut about a million short pieces of 24awg. This sounds not bad, except they need to be straighter than you are capable of making them and have about 1mm of tolerance before they short on the other side. Start by putting solder paste on the LED pads then placing the wires on top.

After doing half a dozen this way, get fed up that none of the wires are flat and will spring up screwing everything in the process. Start sticking the wires directly to the tape, then put paste on the top.