Well, if 24x8 is really desired, this might be a good time to learn about PCB services.
For example, expresspcb.com will make you three 2.5" x 3.8" double sided boards with really fast turnaround for $51. I spent just a few minutes drawing up a bunch of 5mm LEDa on a board - 24 wide won't fit on a board, but 16 will. Stopping at 12 x 8, adding some via & mounting holes, you could mount 2 side by side by trimming the 2nd one (and I even added a couple of lines for a hacksaw guide), putting in 8 jumpers to connect the two and bring all your lines out to 2 connectors to go to your transistor drivers.
Desoldering 2 leads to remove an LED is pretty simple, I've had to do to it a couple of times for bad LEDs, the boards have held up well to reworking with no lifted traces.
Could even move the 8 pin connector over add your current limit resisters there too.