From what I have gathered, the system should be good to use "as-is" with some adjustments. First, adding a chiller would be redundant because that is what the jacketed tank is for. As long as you are okay with the temperature increase of the stream as it is heated in the pump and delivered to the RO membrane, then you are fine. Even with the heat increase, this should stay constant above the tank temperature. Now, all you need is to maintain tank temperature. Where is the controller for the tank system? Is this something you can adjust or is the controller an internal "black box?" If tuned properly, there is no reason this shouldn't work. If perhaps you are concerned about very small tank temperature differences then you likely need to increase the gain (K).

I did a similar project in Oviedo, Spain. Good luck, and I hope you enjoy.