A few suggestions/recommendations:
First, before any game, wash your hands thoroughly with soap and water. I do this because it helps dry out your hands, removes any oils, and helps keep your gloves smelling fresher, longer.
Second, take your gloves off in between shifts while on the bench. I'll usually take one glove off one shift, then the other hand the next. It's only a few minutes, but it really helps your hand breath/cool off and let a bit of air in your gloves.
Third, try Tacki Mac or another tape alternative. I switched exclusively to Tacki Mac and tennis overgrips on every one of my sticks now and the amount of wear on my palms after a full season is what I'd normally see after a single game using traditional tape.
If you STILL have problems, I guess you could always bring a second pair of gloves to the bench and alternate which ones you wear each period? Like already recommended, try pro stock with an overlay on the palms of nash/micronash which will be more durable than some other palm materials. If you like a tight fitting glove, I'd recommend the QRL, but they also run a bit warm so that might not work for you