I'm thinking that if it was me, (which it hopefully will be some day), I'd rather just take the extra flights than skip out on em.
Getting paid to fly anything is better than not, and from what it sounds like, it doesn't accelerate the training a whole lot anyways.
I'd just go with the flow, keep my mouth shut about my civi time, stay away from "well I learned it this way...isms", take the extra flights, and enjoy the extra time in TRACOM's with a few cold ones.
Course I could be off base here.
Bad idea.