Both devices were on the same subnet and had fixed IPs. Everything finally worked when I abandoned connecting to the WiFi of the existing router and I installed and configured a TP-Link mini router in its AP mode. Everything was then configured with the exact same parameters, but with TP-Link AP the TSU9600 would link with the RFX9600 and they would work flawlessly. The lesson and moral of my experience is that if in the RC forums it is stated that APs of different manufacturers can be the issue, one should heed to those warnings and advice.
Thanks again Lyndel.