that picture is eerily similar to my project i just took on. in my boat (same engine, predator 310). and as you guessed, water came in through the exhaust manifolds. your best bet is to get that engine to an engine rebuilder. that engine needs a full rebuild, and most likely several brand new parts.
also, you will be tempted to get a different engine that you may find used somewhere, but trust me, use the same engine. it will save you tons of stress and messing around getting the wiring to work with a differnt engine.
as for removal, you need to take all the seats out of the boat, and part of the floor. the ski pylon can stay, but the seats and fiberglass are easily removeable so that the engine and trans can come out together.