Thanks @dwrowe, I guess at this point people use PCBs but I’ve got zero experience making those, so that’s a project for the future. You mention mosfet chips and I remember VInnyCordeiro talked about those in this thread on in-switch LEDs, so you’ve confirmed that’s the direction for me to go, thanks a lot.
In case it helps anyone else I’ve just found this article on using LED strips for back-lighting.
Thanks a lot for your help, it’s much appreciated.