Homebrew PCBs.... now that's interesting stuff. I've looked a few times at the various kits that are available, but I've always been put off by not actually having a specific project to do. As it happens, I have a large MicroMat PCB drilling rig here at the shed, but it's in a state of some dilapidation, and hasn't been used in many years (at least 10). It's tempting to try to make it work again, as it would make a dandy CNC router; and, of course, well able to drill PCBs...
I know what you mean about LEDs; personally, I'd have used strip board rather than the plain board you've used; at least you can solder the components directly to some copper then, which allows you to fix everything down & doesn't rely on too many hand-wired connections. For your application, you may want to look at using wire-wrap kit instead of soldering everything? That also gets you out of having to make a PCB...