From your web page:
I want to have dynamic wall colours and lighting, according to what is going on in the room.
You realize ( or maybe I'm the fist to tell
) most commercial light panels are specially made laminated plastics which only have LED around the edges. You have seen some. You just may have not noticed.
I have those Adafruit LEDs. And they are bright enough to light up such a panel. The only problem is that the strip is too wide for the types of panels normally used. Such an arrangement will drastically cut down on the number of LEDs used. And, perhaps, solve your power problem serendipitously.
Also note, the current draw from those Adafruit LED strips depends on how many and how bright the LEDs are programmed to be lit. Light 1, 2 or 10 of one color per meter and you can get away with battery operation. Light all of them full on for a "white" color effect and you better be prepared to handle the current.
What ever you do, you will probably be better off distributing your regulators. A heavy current draw over a small resistance can impact low voltages significantly. That is, trying to protect your self from a 1 volt drop at 12 volts is simple. After all, it's less than a 10% fluctuation. But at 5 volts, that 1 volt drop would be a 20% fluctuation! This is one of the reasons most design with at least a 12 volt relay instead of a 5 volt relay.
So, if you use, say, a 12 volt supply, you could use 5 volt buck-converters for, say, every meter of LEDs. A DC-DC converter may be a buck. But some are buck & boost. You don't need or want to pay for the boost part if you only need to reduce the voltage. And, yes, you can go w/an analog regulator (i.e. 7805). But keep in mind each one will waste way way more energy then a buck power supply. (i.e. You'll end up having to buy a bigger power supply just for the 7805s let alone the LEDs.)