I guess that your problem could perhaps be solved by shielding/grounding approaches.
It is more than notorious that the actual assembly with wire-up connections, RF transmitter too close, unconnected pins, and external cable is susceptible to EMI.
Concerning to grounding, you has not mentioned anything about grounding the unused rails of the breadboard, as mentioned before, whether this improved something or not. Concerning to shielding, it could be advisable to use shielded DB connectors, as well as to electrically connect its metallic case of the DB connector to the earth of the PCB ( in your current assembly, the chassis of the breadboard ), once this way all the common mode potentials caught by the antennas effects of your apparatus would be drained to the Earth.
It is more than notorious that the actual assembly with wire-up connections, RF transmitter too close, unconnected pins, and external cable is susceptible to EMI.
Concerning to grounding, you has not mentioned anything about grounding the unused rails of the breadboard, as mentioned before, whether this improved something or not. Concerning to shielding, it could be advisable to use shielded DB connectors, as well as to electrically connect its metallic case of the DB connector to the earth of the PCB ( in your current assembly, the chassis of the breadboard ), once this way all the common mode potentials caught by the antennas effects of your apparatus would be drained to the Earth.