I had a look at an original circuit board from the FX-3 and it looks like I made a mistake. The Vreg in the diagram is just a test point. The actual regulator is incorporated into the integrated circuit and is not a separate component.

I think one could make a tiny regulator based on a Zener diode like this: http://hyperphysics.phy-astr.gsu.edu...c/zenereg.html