Improvise.
Two normal 1.8volt LEDs in series is a perfect 3.6volt zener.
Don't know if it's wise to use the LS family.
Last time I used one was in the eighties.
I use mostly HCTs now.
http://www.adafruit.com/products/1787Runs on fumes, and is not inverting (no library tweaks).
Maybe make provisions on your board to use TWO strip outputs.
You have enough Teensy outputs and level translater ports...
Two the same patterns, or two different ones.
I don't think a TO220 7805 will need a heatsink.
I calculate, with the known parts, ~350mW.
Maybe better to use the 7111-5volt (smd) regulator, and use the ground plane as heatsink.
Leo..