Toro 11-32 rider (model 57360) w/ Briggs 253707-0157-01 mis troubleshooting?

Hello -
Of course this problem would come up when the grass is *really* tall, and I need to mow it before my neighbors kill me.
Anywho, I have a 1984 Toro 11-32 front-engine rider with a Briggs & Stratton 253707-0157-01 (11HP).
Over the past few months it has developed a strange mis, that I thought was trash in the carb. I'm starting to think that's not the case, and that perhaps it's electrical in nature. Here's what I have:

Symptoms:
- Engine will operate as normal, then periodically will start to only fire every other stroke. It's very similar to the way it sounds when you have the choke on and it's not needed. It does start and run, but has no power, and the throttle has no effect.When it does this, it will barely move, and mowing at all is futile.The mower won't die, but will barely move at all.
- When it is doing this, it will suddenly and miraculously start running right (another reason I thought it was the fuel system) for no reason at all.
- This symptom can sometimes be induced by driving over very bumpy terrain, or if I am mowing on an incline, such as the bank near the road, where the left-hand side of the mower is lower than the right-hand side.(this is one reason I originally thought it was in the fuel system).

What I have done:
- I have taken the carb off, adjusted this way and that, put it back on, played with the choke and throttle blades while running, played wit hthe linkage and springs, and none have any effect.
- I have removed the plug, and it is black, so it looks like it's just not firing correctly on a consistent basis.

So all was well until this past weekend. When it would do this previously, I would just wait a minute and it would go away and act normal. Now the thing wants to do it all the time, and I can't even begin to mow the grass.
I tightened the connector from the plug-wire to the plug, and suddenly the thing started running right for all of 5 minutes before doing it again.
I'm starting to think it's either the plug-wire, ignition module assembly, or both.

Can anyone offer any insight? I love the mower for it's simplicity and ease of use, but I need to get this fixed.

HELP!! I REALLY NEED TO MOW MY GRASS!!! :((