I have to agree about the coil. It's sort of an out there possibility but lick Chzekmate, It usually is not the problem.  I've had a grand total of 1 coil in my life that was bad out of all the bikes, cars, lawn mowers, weed eaters, etc.  Plenty of fuel delivery problems though.

Usually a coil either fires or it doesn't.  It won't get hot enough in a few seconds to start acting up if it's heat related.

Do you, by any chance, know what the jet sizes are in your carb?
Someone else already asked and I didn't see an answer, will it start right back up after it quits or do you have to wait a while?

Thanks for the feedback. I'm still tinkering. To answer your questions:

Main Jet 55 and the Pilot Jet 150.

Yes, the screen beneath the float needle has been cleaned. Vigorously.

I tried it with stock jets and stock exhaust. Not as loud but the same result.

Fuel is new.

I haven't blown air through everything in the carb. I will try that next.

I just replaced the Float Bowl Gasket, because it started leaking.

Battery is new and fully charged.

The guy I purchased it from was moving his shop at the same time. He gave me a bunch of extra spare parts: two air boxes, two wiring harnesses, two headlights, some missmatched controls, extra mirrors, etc. Almost enough to have a garage sale!

And yes, I did replace the coil. And, you are right, that wasn't the issue.

I also replaced the fuel line as the other one was starting to get brittle. Still had a little flex to it, but not much. The new one is much more flexable. Hose clamps are new.

I was thinking of scraping a few bucks together and buy a VM carb from Lancer, but I'd really like to solve this issue first.

Thanks for the help.

Any time I don't know what is wrong I just shoot ether at it. If it doesn't burp or fart, eliminate the gasoline and shoot ether at it.
Check the plug, see if it's wet. AFTER blowing the dirt from the recess it sits in.
A spare plug, pull the plug wire, stick it on the spare plug, ground it, hit start. PROVE that the ignition will spark a plug WHILE the starter is under full load.  Yes, that means the plug must be installed.

White smoke or blue? That would indicate oil is fouling the combustion.

Was the bike tipped on it's side at all for a period of time? Oil may have flooded the combustion chamber. Or the rings and or valve stem seals are worn out. Hard to tell without seeing it.

You really need to check the basics first. Valve lash needs to be at .004 intake and exhaust, compression needs to be at least 175 or higher psi to run right.  

White smoke, (not blue/grey)... is usually water vapor...
That may come from sitting in a cool damp place,.. water collects in your muffler and evaporates out when you start up...
Harmless...

You can also get white smoke if you've added to much additive to your fuel... (something like Seafoam)...

From what I gather and your level of expertise you really need to have an experienced mechanic look it over. The basics need to be right or no go.

Valve lash needs to be at .004 intake and exhaust, compression needs to be at least 175 or higher psi to run right and decompression cable disengaging all the way.

Maybe you can find a member in your area and work something out?

I just heard back from my Mechanic. It looks like the Cam Chain is out of adjustment. He wants $600 to do the repair. My question is: is this something I can do myself?