Yep. Choke off as soon as you can. If you wait until ANYthing is warm to the touch (pipe, KIPS, cylinder, head) the choke has been on too long.
The idea of soaking an air filter in oil and then wringing it out has never made sense to me. You're using way more oil than is necessary. With the air filter that soaked (wrung out or not) you are running even MORE rich than the already too rich oem jet-set gets you.
I'd suggest NoToil as an air filter system. You wash a NoToil oiled filter in the sink with NoToil soap and water. Heck...you can throw it in the washing machine if you like. Use NoToil spray filter oil. Spray it just enough to make it pretty much pink/red (the color of the oil), work it in with your hands, let it dry, grease the rim, stick it on. It makes filter service such a breeze that doing it every couple rides won't be a hassle.
That will give you a much better breathing filter and reduce the chances of plug fouling.
You should be running an NGK BR8ES. When you get you're jetting sorted out (and don't foul plugs anymore) a fine wire BR8EG is a good choice. Don't run any other brand of plug (imo and all that). NGKs are great sparkers.
4-stroking is a term used to describe a 2-stroke motor that is firing every other piston TDC (top dead center) event...like a 4-stroke engine does. A 2-stroke normally fires EVERY TDC event. It's a sputturing, gutless, smokin' mess, but it WILL generally clean out if you do a few 'wind sprints'. Open'r up and run it til it quits. Oh...I mean RIDE it..don't just sit still and WOT the thing (that makes me cringe when guys do that!!)
A fouled plug will not fire at all. You won't be going nowhere.
With your description of the choke being on until the kIPS cover is warm...AND a soaked air filter..those two things could be the entire problem.
You could try running the filter with NO oil on it for a bit. I don't mean for an afternoon, but for a couple of those 'wind sprint' runs to see how much difference that makes. As long as you're not riding though a duststorm you won't hurt anything. Keep it to a couple minutes and it will be fine.
You will likely need a new air filter. The petro products in the oil you're using won't get along with the water soluble NoToil. You may still find some NoToil kits that come WITH a filter. They used to do that all the time. They stopped doing it quite awhile back, but I've seen such kits in shops fairly recently still.
If you get another filter (good to have a few, actually), consider a TwinAir.
Wringing a filter will stress the joints to the point you will end up ruining it by literally tearing it apart. Hopefully, you won't find the holes when you're taking the thing OFF your bike!!
Regarding plug fouling in general...I haven't fouled a plug on my bike in years. The last two -EG plugs I've used I've run in the bike about a year. That's a bit long, probably changing it every six months would be a good idea. Obviously depends on how much you ride. When the weather is 1/2 decent, I'll ride 3-400 miles a month. It's not always 1/2 decent..may still ride, just not as far!
What is your airscrew (the brass one) set too? Have you set it for best throttle response or is it just set to some number of turns out?
Keep with us. The folks here can get your bike to running much better than it is now. You won't believe the power lurking in that little green 2-hunny!!
Have fun!!
Let us know how a choke off...different filter works!