Oil/water mix.....
After reading all the post and replies, it seems your having an over abundant amount of oil in the cylinders and your not drying out the combustion chambers.
Are you keeping an eye on the level in your oil tank? Re-post if you've noticed a significant loss of oil. With the amount of oily sludge you appear to be getting, I'm concerned that the oil seal(s) to the rotary chamber are shot.
Since it's been several days and your engine has lubrication, it may be time to start disconnecting some of your components to clean out your exhaust, combustion and intake systems.
You should have your air induction cover (black plastic) removed. Take out the 6 screws and remove the flame arrestor. This way, you'll expose the throttle plates. Look inside, what do you see? If the throttle plates are showing signs of rust, spray a dab of WD in it..........don't over do it. Sounds like you got enough oil in the motor for the moment.
The next thing you can do....and this is just temporary, pinch the oil line going to the rotary chamber. This will stop the oil from getting into the combustion chamber if there is a bad seal.
Make sure your fuel is in the off position. You don't need anymore liquids going to the motor.
Try spinning the motor over again for several revolutions to see if you can expel the oily sludge. If you get to a point where theres not a lot coming out, then you may be o.k. to try and fire off. Like "gunsrunner" said, if you can get this thing started, then the heat off the engine is going to dry the rest of it out.
In extreme cases of hard sludge, you may want to put in a half cup of fuel/oil gas mix in each plug hole, then role the engine over several times, expelling the mix. The fuel will help cut through the sludge and remove it. Make sure you put a rag over the spark plug holes to catch the blowing discharge.
The idea that the pressure from your cylinders can't expel water in the exhaust system is incorrect. IF your compression is good, this shouldn't be a problem. You won't be able to expel it with the plugs out though. Which brings up a good point. If you still have material in that tuned pipe, you may need to put the plugs in and roll the engine enough to expel what's in the exhuast system and resonator.
Your also at a point where you my find yourself removing the head cover. In doing this, you'll be able to check the pistons and look for any signs of damage from the water. You'll also be able to roll one piston at a time to the bottom of its travel and use some type of siphon (I use a shop vac with a 1/2" hose taped to the end. If you look at the bottom of the cylinder, you'll see openings in the cylinder sleeve. You can use this hose to push through into the bottom of the crankcase and suck out any excess that is in the bottom. If the oil and water has created a sludge, it's heavy and will settle in that combustion chamber.
Lastly, that balance shaft that Karl has told you about, if water has crossed those seals and mixed with your 30 wt motor oil, then you will have to do what you can to take as much out as you can. It only holds an ounce, so you may not get much. Just make sure it's topped off. Once the engine is running and heats up, the moisture in that oil will also evaporate. But you'll have to check it again after your running.
There are a lot of good response here to your problem. In my reply, I don't expect you to do all the above referenced work. It's just some ideas for you to ponder if you think you've done everything else. You can use what you want and dump the rest.
If this was my situation (understand, I'm a backyard-shadetree mechanic) and I was having a problem with this much sludge, I'd drown the engine in a liquid degreaser.........pouring it in quite liberally. Then, slowly turn the engine over by hand at the rear shaft to stir it up and help dissolve the sludge. Then, after rolling it over by hand to the point most has expelled through the cylinders or exhaust, I'd spin the engine over, then put the plugs in and spin it more.............
Your doing good, keep the engine from locking up!....that is the most important. The second is the electricals and you've said you got spark.
Remember, if you pinch your rotary oil line, don't forget you've done it.
Sorry for the long reply, but it's part of what I do..............I talk alot!:cheers: