A simple way that will allow Linux Synchronet to run completely as non-root is to explicitly allow the binary to bind low ports using the setcap command.
sudo /sbin/setcap 'cap_net_bind_service=ep' /sbbs/exec/sbbs
This must be ran on the binary itself (if /sbbs/exec/sbbs is a symlink, apply it to the target of the link instead). This will need to be re-ran any time the binary is rebuilt.
A better alternative may be authbind: