Just a thought here, but wouldn't bad gas run rough at almost all RPM's?
It will start, and runs fine at normal RPM's, but when I slow down to no-wake or idle, it stalls. It will restart but immediately stop unless I advance the throttle, and once I get up to speed it seems to run ok.
This sounds more like a clogged Pilot Jet, than bad fuel. The pilot jet would be used to deliver fuel at idle, while the main jet will deliever fuel on throttle (technically the pilot always delivers a fixed amount of fuel). As teh throttle is opened, the main needles should get slowly lifted from the main jet. Both the main and needle are tapered and should increase fuel exponentially as the throttle is increased. A the same time, the throttle body should be openeing the air aperture to maintain a balanced fuel to air ratio.
When I hear a description like this, where at idle it stalls, but slightly advancing the throttle allows the engine to remain running at idle, it sounds an aweful lot like the pilot jets are clogged and the main jet needs to be opened slightly to compensate. The clogging can absolutely be a result of old gas sitting in teh carb. Especially if the engine wasn't run long enough after adding the fuel stabilizer to purge the gas in the fuel line and fuel bowls on the carb to replace the fuel in the fuel bowls with the stabilized fuel. (On motorcycles, I shut off the fuel and run them dry to winterize).
Carbs are carbs whether they're in boats, bikes or cars. I would suspect a clogged pilot jet, based on this description.
Just my .02 I'm very curious to hear feedback from the poster on this one.