Well, when the ignition transformer failed in mine, I found a Beckett solid state oil burner ignitor module for less money than the replacement transformer from Desa. Since it had more than twice the voltage, and two floating terminals (so no spark to ground), I figured I could shoot for a bigger spark gap. One that went right across the spray cone.
So, I took two old spark plugs from my car, and carefully sawed off most of the threads so I had a long ceramic insulating cone with the electrode sticking out. I drilled out the opposite side of the "bridge" that the spark plug was in, and put one of these plugs in each side, and hooked up each plug to a terminal using old spark plug wire (you need that silicone insulated stuff to resist this kind of voltage). The result was a 1/2" arc that fired across the front of the nozzle, which would reliably ignite diesel (which I really wanted to try, because I had trouble finding kerosene for a reasonable price locally).
Really, it's just a homebrew clone of how an oil burner works.
What I discovered though, was that no matter how I tuned the adjustments, I could not get a clean enough flame with ULS diesel. Either it was spewing CO when it was rich, or it was making so much NOx that it would burn your eyes when it was neutral or lean. Then, when it got really cold, it was smokey, so I even tried an oil-pan heating pad under the tank with no luck.
Worst than all of that though, was the smell. It would linger on your clothing even after washing it, and was very difficult to wash out of my hair.
Since then, I've found a pump source for kerosene which is 1/4 the price of buying it by the gallon in the store, so I just gave up on diesel.
As for the filter. You could probably order one. There aren't many sizes. You probably either have the round pump with the D shaped filter, or the rectangular pump. Either way, I'd just go to the hardware store and pick up one of those green foam air filter covers (one that's at least 1/2" thick), and cut it to fit.
The spark plug will always build up black stuff that looks like it is running rich. This is not burning gasoline. If it's not making -some- soot, it is too lean.
I'd suggest just giving it a brushing once a year.
The hot wire style ignitors don't need cleaning, but they're really fragile. What you have is better.
Try some new kero, and if that helps, just slowly burn up your old stuff, well diluted.
. I don't know if it's a nice fog. I tried to start it without the inlet filter and no go. I tried it again tonight, put the filter in part way and it fired. I think I'm going to go get some good kerosene, try and find both the inlet and outlet filters. What was your wacky mod?