Checked baggage can have unfrozen meat and liquid blood. However, make sure whatever cooler you use doesn't leak or they'll throw it out potentially hold you liable for anyone else's luggage you "contaminate".
Dry ice in checked baggage only, no more than 5lbs, must be able to vent. No liquid ice.
Big heavy rotomolded coolers are for truck beds, not airplanes. If the meat is already frozen, a Rubbermaid tote works just fine. It'll weigh less and hold more meat. I flew 20 hours from Hawaii with frozen meat wrapped in clothes in a tote and it was just starting to thaw when we got home.
You can bring frozen meat in your carry on or personal item as long as it's rock solid. No one weighs your personal item and carry on. With a little creativity, you can fit a lot of meat in those without worrying about keeping them under a certain weight limit.
Have a roll of duct tape on you to tape the snot out of everything in the airport after weighing all your bags. If you tape it ahead of time then have to shuffle stuff around at baggage check, you'll be in trouble.