As if by magic, I added it to HomeKit fine and the Eufy app sparked up all on its own and connected.
Well done! Glad it’s working again 
After a dozen tries of the “Reset” loop, I tried what worked for you: added the hub to the Home app. It worked. Then, just like for you, it added the hub to the Eufy Security app as well (all by itself). Stupid, but effective. My confidence in Eufy in the long-term is not great. I wish Apple would develop its own HomeKit accessories that “just work.”
Nope. 
Just after restarting the HomeBase, the two eufyCams will briefly appear in Apple’s Home app for about 30 seconds. Then they magically disappear.
After 1 year now of constantly trying to make these cameras work reliably with HomeKit, I’m giving up. The EufyCam works very reliably in it’s own app, but the Apple HomeKit integrations is nothing but painful headache.
Stay Away!