There is no way conceivable possibility where I would leave the heart behind. As far as I am concerned, this is the very best cut of all.
I would recommend that you carry as much water with you as you can stand. Even a couple 20 oz bottles will make a difference if you have to wash out a body cavity. By getting the body on a steep slope or even hung up allows it to drain better. Use handfuls of dry grass to mop up and wipe out. Open your water bottle and put your thumb over the neck of the bottle and you can squirt the water in a controlled stream and in small bursts. Dump out the small amounts of water that gather in the cavity often. Ration the water and splash it where it will do the most good. The sooner you get to where a hose can finish the job, the better.
Sometimes I keep a 5 gallon bucket of water in the Jeep on hunting trips. The lid has a small hole with a 1/4 inch brass hosebarb and 6' of cheap tubing. A second hole has a 1/4 inch machine thread bolt you can remove it to avoid vapor lock. I can set the bucket on it's side on top of the Jeep and get pretty good pressure for washing up. I used to have the hose barb screwed into the side of the bucket down low, but I kept knocking them off and getting water everywhere!