While it's more fun to just mess around, here is how to successfully complete the surgery: first, use the hammer to smash open the ribs by tapping repeatedly in the center (better than bone saw, trust me). Then, grab and remove ribs/lungs. Use a scalpel to disconnect the old heart and pull it out. Then, throw the new heart in and try to line it up with the old arteries. If it doesn't give you the success message, jostle the heart around/pick it up and drop it repeatedly until it lines up.
My strategy for beating harder: Recruit people and recover housing squares as often as possible. You want your population to always be full. Don't worry about farms so much, and scavenge food when you have to. Pick a city where you can get a school within the first couple turns; make everyone but a couple builders and leaders into soldiers as soon as they arrive. Try to quickly get a hospital and a lab as well; research zombie vitals and then food options. Get to a side, spread along the side to a corner, spread from the corner. Find an ending square and spread to it; do the ending. Do the other endings if you want.
Tips:
1. *Most important* You have to be buying tea pretty much the entire time, every 2-3 seconds, regardless of price (don't go too fast or you will drive it up sharply)
2. Trade like a bandit while you have the bribe card - it expires near the third quarter of the game so you should use it up
3. Each commodity has a pattern for its price that is mainly steady between the games; try to learn it
Eh. Confusing interface, awful unmutable music, physically painful voice acting...Not even the badges makes this one fun for me. Glad some other people like it.