Unable to su into any user

You can use AllowUsers / AllowGroups if you have only a few users/groups that are allowed to login via ssh or DenyUsers / DenyGroups if you have only a few users/groups that are not allowed to login. Note that this only restricts login via ssh, other ways of login (console, ftp, ...) are still possible. You need to add these options to your /etc/ssh/sshd_config file for most ssh installations.

If you have set the login shell to /bin/false you can use su -s /bin/bash user (replace /bin/bash with the shell of your choice)

Due to the limited information, I am not going to theorize in detail as to the potential security implications of your architecture. However, I would be especially cautious about granting the ability to add users to a non-root user.

With that said, I would discourage the use of the SUID bit for that purpose. If nothing else, because it introduces additional exposure to every user on the system. Meaning, every user could potentially add users.

As an alternative, you could configure sudo to allow the non-root user to run usermod. For example, run visudo and add this line:

redmineuser ALL=NOPASSWD: /usr/sbin/usermod