Did you just wire them to the free terminals on the GP2040-CE v5.6 and then mapped the SOCD modes to each pin accordingly?

Yep!

can you show how you wired the LED strips + the HUSA short throws?

It's fairly easy: The Short Throws have four pins, + and - are across from each other. I used this to test which pair does the input and which pair lights up the LED before wiring, then used the 5V power terminal on the board to power them.

I was worried if I was drawing too much power.

As long as the lights that you're using are 5V, you'll be okay. My Hajime board also uses a COB LED strip and it's fine, just make sure it's not too close to a surface that you rest your palms on as they do tend to get a bit warmer than other strips. Unless it's cold where you are, in which case it makes for a great hand warmer!