Anything with citric acid seems to help with bleeding, also (my experience).
I had stomach surgery a couple years ago, so I can't have sugar OR carbonation. I no longer have sodas in the boat (used to have ample supplies of Mt. Dew for me as well as any fish that were in need)...
But, I've come to find that the Vitamin Water Zero drinks I keep in the boat also help with bleeding.
On the rare occasion I have a deep hook situation:
1. Take extra care to pull fish from the water by my hand under the belly (instead of swinging)
2. Hold my breath (I thought I was the only guy who did that?) to steady my hand (as well as help keep in mind that my aquatic friend is holding his breath too) while I turn / remove the hook.
3. Pour some Vitamin Water in his mouth (heck, I pour some on his side if he has any sores).
4. Let him rest in live well (Rejuvenade - if water is over 80°, there will also be some ice packs in there).
5. Check on him in an hour or two (usually he's good to go within an hour); and release.
Even if it's a short fish, I'll still put in the live well. I haven't ever been visited by an officer while I was recuperating a fish, but I'd rather explain / show what I'm doing to the officer than just cut a hook and hope for the best.