Thanks for all the input / advice. I have now solved the problem.
I switched from using the DRA818V Transmitter Module to using the SR_FRS_1WV Transmitter Module and redesigned my break out board around it.
I also included a Low Pass Filter (Mini Circuits LCFN-160+) between the Antenna Pin on the module and the SMA Edge Connector and then finally, I used VIA stitching around the outside of the antenna trace on the PCB from the Module's Antenna Pin all the way to the SMA connector.
I couldn't tell you which of those steps was the actual cure. Maybe it was one thing or maybe it was everything combined but it all works now. I also no longer need to exclusively house my project in a metal enclosure to combat RFI. With this new module and setup, I can transmit without the project being in any box and I get no interference at all - much to my amazement and delight I might add!
Also for the benefit of anyone experimenting around with these transmitter modules, I can highly recommend the SR_FRS_1WV over the DRA818V. The SR_FRS module is half the price of the DRA818V and in my personal opinion, the SR_FRS is much more user friendly and the audio quality seems to be far superior as well.
Thanks again!