Next time you are at a jam, ask if you can play through one of the vocal mics. Ask the guy at the board to roll off frequencies above 5 or 6k. That possibly will work well to increase volume and minimize key click.
By the way, on some songs (groove oriented or even some blues numbers) you may actually want to incorporate key click into the sound as a percussive effect.
The electronically-generated key click on a Hammond organ is considered an essential part of the sound. So much so that the digital Hammond organs have settings to vary the amount of click, both “key on” click and “key release” click.
Generally, I do not like the mechanical key click sound on my melodicas either. (Although I may but it to good use on a selected song or two.) But when you are squashing all the high end frequencies like I am currently doing, it is a non issue. There is very little if any key click to be heard no matter how hard you play.