Thanks for the prompt replies. As soon as I added a second ground plane it all came together nicely.
Regarding two ground planes... I've read forum posts were people mentioned that putting two ground planes could turn the board into a big capacitor and provoke undesired effects if you were not "careful" (not sure what their definition of careful was). On the other hand, the argument against that was that since these were two GND planes, there is no voltage difference therefore they couldn't form a capacitor. And yet again, the argument against that was that in reality there might be a tiny difference in voltage so we're back to square one.
My only interest in PCBs are at the hobby level so should I be worrying about these kinds of nuances? Or do you think I'm better off slapping two ground planes in and forgetting about it?