Hi Kris,
After permissions are corrected logon to all three your system DEV/QA/PROD and make sure in the RFC in sm59 for all rfc's TMSADM@ that you check the logon and security tab and correct the passwords for the user in this section on each target system.
Once you can test all the RFC's successfully with authorization check i.e. Utilities -> Test -> Authorization check you can retry and you should be able to approve your STMS configuration.
Kind Regards,
J