Dear Ryan,
It is not possible to establish TCP connection without the 3-way handshake that starts with a syn packet.
The rule you provided drops the syn packet (except on port 80) and this prevents the connections from being established (including ssh).
The only way to accomplish what you are trying to do is either to create an allowlist of IPs that can access the services and the rest are blocked.
Or by implementing some network level authentication mechanism (eg: port knocking) which will again requires that you define/customize you clients.