I've done this 4 or 5 times and have not found a way to not have some mess.
At the dock, I used a radiator flush kit from the auto store. You can put this inline with the hose to the water heater. I then removed the thermostat and flushed water through the system collecting it in buckets for disposal until it was clear. Then I just dumped the buckets out on the ground. Then I used a drill pump to push coolant into the system. I still had some air-bound issues doing it this way I had to deal with.
Next time I just used a drill pump and had buckets to collect the coolant and water to push through the system to flush it with the drill pump. Worked fine but still air-bound issues to deal with.
My current method is to drain the system completely just using drain plugs and removing hoses. There is a drain on the heat exchanger, a drain on the block next to the head bulkhead and then draining the water heater is a pain. Yes this makes a mess and some coolant gets in the bilge, mainly from the water heater. I will use a shop vac to help drain some of it. The coolant from the block goes into the engine bilge and can be pumped out for disposal. I have installed the "MaineSail" system for burping the system and getting out the air and its simple. You can get the best procedure that works for me from the
C34 Tech Wiki. Response #14 has the "MaineSail" system.
A good thing to remember is that the C34 essentially has the same engine as us. So a lot of the Tech Wiki stuff is directly applicable to our engines.
Something interesting I found a couple of months ago. The engine was getting a little warm but the coolant level in the tank wasn't changing. I found that the hole that goes from the pressure cap to the coolant tank was blocked. I used some small drill bits turned by hand to clean it out.
Good luck and fair winds,
Jesse