After a couple weeks with no time to dedicate to these, I have an update:
On the Drillgine, I had to reinstall the starter pull cord and also fix the end of the recoil spring that sticks out through the blower housing so it would stay in place. Then with the new diaphragm in the carb I was able to get her running. Chucked up a 3/8" drill bit and drilled some holes through a 2x4 to see how it ran under load. Runs nicely.
On the Tiny Tiger, I had taken some carb parts and used them to get the Drillgine going and needed some other parts. Wallfish is in the process of shipping me parts he had this week. Hopefully that will get me further along to the point I can try to start it. I still need the wooden handle for the pull cord. It is the wooden longer black handle with ball end. Would anyone have dimensions they would share with me (Thanks again DustyB for the awesome base diagram!) I'll need overall length, shank length, and diameter of ball end. If someone provides this information, I'll try my hand at turning one on the wood lathe.