Okay - I think I may have had several problems original and have gone down some wormholes....
I think I originally had both a carburetor problem (blockages at fine air intake hole - known for causing surging and bad o-rings around the jets - they were loose originally and fell out of tube cover when turned upside down).  Combined with a fuel delivery problem.  
 
I have placed spark testers between ignition coils and plugs - I'm getting spark when I turn the ignition.  I also unplugged the pressure switch, but this made no difference (and when plugged in I'm getting spark).  So not the problem.  Moreover, I can hear the fuel solenoid click so it is getting 12VDC when key turned.  Also I test visually when the bowl was off the carb.  
 
I did put in a new fuel line and now it seems there is barely a trickle of fuel at the height of the carb gas intake - see video and pics of fuel line (evidently I cant upload video - with fuel line low to ground, fuel flows - but at same height as carb gas intake, fuel slows to a trickle or stops).  This fuel line was made from exact length of original.  Fuel filter has gas in it, but there seems to be little flow to carb.
 
The manual for this engine (44N777-024-E1) shows a fuel pump, but I assume this is an option depending on where individual manufacturers place the fuel tank - in my case...up behind the engine.
 
Any suggestions on fuel line length or increase pressure - gas cap in loose, but makes barely a difference.
 
Is it possible to retrofit a fuel pump on this to ensure delivery - i.e. breather in valve cover and mount fuel pump between filter and carb?
 
Thanks.
 

Okay - just saw this after I shortened the fuel line about 3-4 inches.
It fired up and ran (with choke) - but the moment I would push in the choke, it would start to die.  Pull the choke on...it would run better.  Squirted some carb cleaner into the air intake and it would improve.
That was the first time - second time I was able to unchoke it but then the governor would start to 'search'...I sprayed carb cleaner all over the gaskets around the carb - at the intake manifold, air elbow, and cylinders - nothing.  It would search and back fire (I think because of carb cleaner - had not done this before).
 
I got some good video but I can only upload pictures.  Don't know where else to check for a vacuum leak....

Actually...I should say...
 
Keep the jets on the tube original....
 
Drill out the carb body - i.e. the small holes (left and right) below the emulsion tubes that feed the channel under the plate/cover on the other side that feed the holes to the barrels.
 
Stock = 0.020" (#76 drill bit)
Modify to... 0.0292" (#74 drill bit)
 
Maybe start with a Chinese $30 copy since on carb body...haha

Thanks.
I've decided that before I drill out the low side jets...I'm going to give it a go cleaning EVERYTHING **AGAIN**...
Going to try soaking in Pine Sol and then rinsing in water and then blow out with compressed air and then blow out with carb cleaner/WD40.
If that doesn't work, then I'll try to open the jets up a little bit to like a #69 drill bit.
Thanks.

Any updates?
 
 
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You may want to check fuel flow (mentioned earlier) at each point starting at the tank.
IE; just before the filter, just after the filter, just before the carb... You should have good flow
at all points.
 
If there's a restriction at any point the new pump may have issues over coming it.
 
The carb bowl, being mostly dry will cause the issues you previously described including surging (running lean)
 
Please post back what you find and any updates..
 
 
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Yea!!
 
Yep, that tank isn't much higher than the carb...
 
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