Asthmatic Engine
Greg,
Sounds like the engine isn't breathing well. Black smoke usually indicates a lack of oxygen or an inability to dispell exhuast gas (i.e. can't breathe in or can't breathe out).
Although you checked the air filter (is it the correct one?), might try a new one as glass fibres, small particles and dust may still be plugging it, especially if its old. You can always run the engine for a short period without the air filter (just make sure nothing can be sucked in) and try it that way to see if it gets better. Also, try running engine with engine box open and see if that helps any. Maybe the box is starving it for air (recent sound proofing? or other box modifications?).
Think back and if there is anything that was done to the engine or location that may be a tip off of where to look.
If nothing there, try poking into the exhuast system. Look for collapsed hoses, excessive dips where water may collect, check the aqua lift for crud and sediment (may have built up and choked off the exhaust especially if operating in shallow or muddy water). Look for rusty pipes (it will be same if not worse on inside). A collapsed hose is a possibility especially if 10 years or older. I've seen delaminated hoses that looked fine outside but collapsed inside.
Have the valves been checked lately? If the valves are not lifting all the way up, then the engine will starve that way. Do you have a sea cock on the exhaust outlet? check that as it may be partially closed or broken off..... As you said, the flapper may be stuck.
As someone else said, it may be overloaded from growth on the wheel or a line wrapped around it (or something else like a garbage bag). When's the last time the cutlass bearing was changed? Might be very worn and jamming the shaft..... Check to see if the shaft spins easily with your hand (engine off of course). Power on Vs. Neutral is a way to check that area.
There are all kinds of things to check, but start with the easy things as that usually solves the problem.
John M.