This is untested, but setting up something like this at the very end of
sshd_config should work:
Match Address 192.168.1.0/24
Basically you're globally allowing public key auth, globally disallowing password auth, and then specifically re-allowing password authentication for anyone in the 192.168.1.0/24 subnet.
You probably already have the first three lines elsewhere in your config. If you do, they do not need to be added again. However the "Match" block must be at the end of the file.
RSAAuthentication keyword is specific to SSH v1, which you don't allow, right?