You all have been great with your assistance!
I finally had a day off, so I could submerge myself into this problem.
I had time to do a little research on two-stroke engines. Given that 3 things are neccesary for motor operation (compression, fuel supply, and spark), I worked on ruling everything out. I had spark, and compression, so I knew that fuel delivery had to be the culprit.
I've taken-apart carburators before from old cars, and never have been consistently sucessful on getting the car to work as desired afterwards, so I had very little confidence that this tear-down/reaasembly would be sucessful.
Norm's "Total Carb Breakdown" gave me the initial interest on what to do. I was also fortunate enough to be able to speak with Duane from ThatsDax, when he gave me confidence tear-down my only
carburator on hand, by emphasing the simplicity of its design. I was relieved to see that I had all kinds if "junk" in my carburator, in both the needle-seat and jet, along with other stuff sitting in the bottom of the bowl. (Wormy bugars).
I ordered a shelf carb from ThatsDax, in the event of unsuccesful cleaning. (I had nothing to lose at this point).
A word to the wise: Always install a good inline fuel filter before starting-up for the first time. I purchased my bike used, with a dirty carburator, and it gave me all kinds of trouble. I was very confused, trying to blame everything from the CDI, to the throttle assembly.
I disassembled the whole carb down to the last screw, and blasted everthing-out, from head to toe, with Gumout carburator cleaner. Duane emphasised the important stuff to watch for, like being able to see a nice, clean tunnel through the jet and needle seat assembly. )By the way, eye protection is highly recommended when blasting the ports/jets with the plastic straw.)
A see-through fuel line, and fuel filter made it easy to verify proper fuel delivery. The tickler was also very handy for refilling the bowl. I'll bet that's the only purpose for the tickler button.
After cleaning-out the carb, installing a new inline fuel filter (Briggs and Stratton), and flushing-out my tank, I knew there was no way that engine could fail now. All three elements: compression, spark, and fuel delivery were present. I told my daughter to plug her ears (muffler-off), because there was going to be some loud popping about to happen in the basement. Sure enough, that baby fired right-up. (default clip setting [2'nd notch], and 3 turns-out ffrom full seat for the idle speed needle).
It now starts whenever, hot or cold, and wherever I care to. I'm no longer fearful of turning off my engine, for fear of having to spend a mile or so restarting it.
Thanks to Duane (ThatsDax), and Norm, for the pictorials. I'm kind of liking this hobby, and now new hope is restored for realizing a savings from the 150 miles/gallon savings for commutes.
ThatsDax highly recommended!