Reins Snap Bit

My mare wears a rubber mullen mouth pelham and goes wonderfully in it- enough stopping power with an adjustable, delicate touch (I ride with two pairs of reins). As she is in re-training after an injury and was just getting steady with giving her jaw and holding a nice, down and relaxed headset, Foxie is just starting to come back into going on the bit. She responds well to a light side to side work of the reins, as well as a give and take on both reins, but really seems to snap into "good horse" mode when she starts chewing and slobbering. Is there any way to make a rubber bit more acceptable/palatable? Or to encourage chewing/loosening of the jaw?

Thanks so much in advance,
Rory