Relay contact sticking while driving a capacitive load
You might want to use an inductor after all. Besides limiting the inrush current, it will improve your circuit's power factor which right now should be reduced by the capacitive nature of the load, at least judging by your description.

Of course, you'll need to find out how much of capacitance you have to counter to calculate the right inductor value. You'll have to either obtain that information from the datasheet or measure it. If you can't, just pick a value and try it out (I'd expect something in units or tens of mH to work).