The great Atomic 4 Disaster of 2006 was temporarily resolved last night. My troubleshooting genius father-in-law pointed me in the right direction (not underwater but towards the electrical system). He still had me check the prop but I think that was just to teach me a lesson.
I fixed the symptom by pulling out the spark plugs and cleaning the carbon buildup off of them (an old vespa trick of mine actually). The engine ran fine in neutral then actually made headway when going into forward (well, actually, it just strained the dock lines and reduced the expected lifespan of my cleats).
One of three things could be leading to the fouled plugs: 1) bad ignition, 2) constantly running at low RPM, and 3) lean fuel mixture.
Possibility number 1 is easy to fix and should be done periodically anyway, I'm switching to electronic ignition, getting new cables and new plugs. Number 2 is quite possible as I rarely use the engine for more than getting in and out of the slip but Marvel's Mystery Oil should help the carbon buildup and I will now resolve to motorsail when going to Angel Island. Number 3 requires being a contortionist to get to the freakin' carburetor but at a minimum I'm going to replace the fuel filter and try to get into the carb to clean out the main jet.
As an aside, on Saturday I couldn't think of a 2-person solution to get out of the slip with an acceptable margin of error. Great suggestions to recruit someone on the dock, but the A dock at Berkeley just doesn't have that kind of foot traffic.
Since then I realized that one person standing on the bow with two long lines tied off to cleats in a V pattern would work. Let the wind back us down, keep us centered with pressure on each line, let go of the starboard line as I turn the tiller, let go of the port line as we clear the slip, grab the boat hook (conveniently laid out on deck) to push off from the piling (just in case) and we're off on a beam reach. There is still a lot that could go wrong but I think there's a contingency plan for most of it.
Not that I have to worry now, I've become a qualified A4 mechanic.