I do not believe your issue is "load" related. I believe instead it's the electrical noise that is created by the AC coil. Maybe removing the loads somehow removes the noise, not sure how but could be. Stranger things have happened.
How about putting a diode (maybe even a cap across the diode produced dc) in series with the coil winding? Just a suggestion
That link might have been where I read about the issues with AC coils.................
Second thought!!!!
I assume you know 120Vac is an RMS voltage
Actually it's 340VAC p-p or 170Vac peak a diode and cap will produce about 170Vdc. Please check your relay specifications before doing the above suggestion. The result could be smoke and fire
