Well, grumpy or not, biting is never acceptable. I appreciate that you are sensitive to his needs and understanding of what he might be saying by this bad behavior, but it is not good to allow it. If you leave him in the frame of mind of wanting to bite, then that emotional state only has more opportunity to become rooted.
If he bites or attempts to, I think you should move him out and get him thinking more about how to survive your driving him around. You want to make him be more aware of and respectful of you than he is sitting around grumping. Give him a sharp reprimand and make him DO something else, so his mind leaves the "funk".
Horses live in the present, so if you make him think of something else, like "MOVE! NOW!" , he will completely forget that only a moment ago he wanted to bite you. It's discipline, and it's a kind of freshening of his mind, believe it or not.
A member said here recently, "if you allow your horse to stand by you and be nervous, you are teaching it to BE nervous". I take that to mean also that if you allow your horse to stand by you and BE in a grumpy state, you are teaching it to be grumpy.
Along with disciplining the biting (dont' be swayed by pity for him and his hard job), if you can take him out for a good gallop, this will really freshen him. Something that makes him breathe hard and breaka good sweat.