haha, well, i'm by no means an expert and others should feel free to chime in and correct me or add anything they might think is helpfull!
for me, it's all about eliminating things as you mentioned aswell.
i wish i could see the spark plug close up... it's not uncommon for a fouled plug not to spark, even out of the combustion chamber. the fact it's not sparking after awhile could be a spark issue but if the plug is appearing to be black and sooty possibly from oil or, wet soaked from gas after a relativly short period, i'd take a close look as to why that's happening. does the plug smell like gas? you can cheat the main with the needle to some extent but the fact that it seemed to make things worse has me scratching my head. but then again you say the plug is covered with black soot..? [ possibly rich]
something i have done quick and cheap to check spark quality is snap off the ground electrode from an old known good plug. if it jumps that gap... i call it good.
i'll try to tag a link to reading plugs here >
Spark Plug colour color guide and engine problem chart
what one do you think best represents YOUR plug?
i have read some of your issues with this machine... it can be frustrating but keep your chin up, you'll get'er!