Here's a procedure that ended up working for me:
Start ZeroTier (ZT) with these two:
cd /var/lib/zerotier-one
sudo zerotier-cli -d
Successful output is: 200 info [Device ID] [version] ONLINE
If you donβt already have a ZT network, create one at my.zerotier.com. Then, over to the Pi to join your network:
sudo zerotier-cli join [Network ID]
Successful output is: 200 join OK
Now, back to the ZeroTier web control panel, networks tab, select your network, and scroll down to the Members section. The Pi should appear as a new device, which you can authorize to access the network by checking the box in the Authorize column.
On the Pi, check that the network connection is successful:
sudo zerotier-cli listnetworks
A good connection gives output: 200 listnetworks [Network ID]... OK PRIVATE ...
Configure the system to run ZeroTier at boot:
sudo systemctl enable zerotier-one
Set up ZeroTier to join the network at startup:
sudo touch /var/lib/zerotier-one/networks.d/[Network ID].conf
Reboot the Pi and verify it connected to the network:
sudo zerotier-cli listnetworks
If connected, the output is: 200 listnetworks [Network ID]... OK PRIVATE ...
All done. Now you should be able to join that ZT network with any other device anywhere in the world and access OctoPi as though it were on the local network. The zerotier web control panel will show the Pi's IP address, but octopi.local
should also work.