I did a fresh install just because I've exhausted all other options the past two days now; and it seemed to work!

GridCustomLayouts is still out of date, but now when I load out of date addons I get the Custom Layouts button in the UI (and as seen on Fenril's picture; it's huge, so no I didn't just miss it).
Appearantly I have to pick "load out of date addons" everytime I login now(?), wasn't the case last time I played WoW (over a year ago though), but since it works now I don't really care.

Thanks for trying to help me guys! Been reinstalling Grid & GridCustomLayouts, as well as trying other addons, like a mad man the last two days.