This seems to be the simplest pattern for getting remote access to your LAN. It doesn't require access to the LAN's router or have some of the pitfalls of bridging. This requires a Linux PC or VM, something that runs iptables, on your LAN. A raspberrypi works. This is a NAT/Masquerade setup.
No broadcast/multicast across networks (but the mobile OS's don't allow this anyways).
Can't initiate connections from the LAN to an external ZeroTier client.
This adds another route to every device joined to the ZeroTier network.
Configure the destination route as slightly larger than the actual physical subnet, here /23 instead of /24 (a smaller number is a bigger subnet in this notation) This makes devices that are on both the physical and the ZeroTier network prefer the physical connection.
Enable IP forwarding
This can vary depending on linux distribution. Typically:
Edit /etc/sysctl.conf to uncomment net.ipv4.ip_forward. This enables forwarding at boot.
To enable it now
sudo sysctl -w net.ipv4.ip_forward=1
Assign some shell variables (personalize these)
Add rules to iptables
sudo iptables -t nat -A POSTROUTING -o $PHY_IFACE -j MASQUERADE
sudo iptables -A FORWARD -i $PHY_IFACE -o $ZT_IFACE -m state --state RELATED,ESTABLISHED -j ACCEPT
sudo iptables -A FORWARD -i $ZT_IFACE -o $PHY_IFACE -j ACCEPT