Codes? Big fat air leak causing a rough idle? If it's getting air in, flooring it should make the rough idle disappear more quickly. The system can handle a small amount of air as there is a return line from the IP and from the injectors. But if you gen enough air in it, it will have to self bleed which goes much faster when you inject more fuel-flooring it.
What I would *guess* is that there is a small leak that when you shut down is letting all the fuel run back into the tank, and filling the line with air from something getting damaged during the airdog install. Like a banjo (if they don't eliminate them-can't remember) fitting, washer, bolt etc. The banjos are easy to damage, that's why I'm quick to point the finger at them.
I can't see how the water could play into this, but I guess if you find an excessive amount of water when you hit the little yellow lever on the fuel filter/water seperator, that should be dealt with.
I doubt the stack backpressure could cause this problem from water in it, but I'd personally be tempted to put a little pinhole in the low point on the exhaust to let it drain. Just in case you park under a downspout or something. Give it SOMEWHERE to go. It would probably take a lot to fill the exhaust far enough to hit the turbo, though. Unless you have a hood stack.