H35 Generator Wont Start at Full Throttle

I'm working on a 1969 vintage Craftsman 1250W generator with a Tecumseh H35 engine. 
 
When I got it, it would start and run for a few minutes and then die.  I wouldn't say it was easy to start, and it was impossible for a few minutes after it died.  I cleaned the carb (but did not put in a kit), and I changed the coil.  Along the way, I had trouble getting the flywheel off, so I tapped the puller holes and in the process destroyed the points, so it now has new points and a new condenser. 
 
I put in a cheap Chinese coil, the current Tecumseh coil doesn't actually fit, the small wires come out on the flywheel side and get chafed (ask me how I know).  The Chinese coil doesn't fit very well either, I had to wrap a wire over it to hold it in and insert a couple plastic shims so it's tight on the core.  When I put it together, it was very difficult to start, but would run OK once running.  I reset the timing (multiple times), trying .065 in. BTDC  (spec) and now it's at .035 in. BTDC.  Now I've changed the carb for a cheap Chinese carb.  Today I checked the valve clearance and made sure the breather was not plugged, there is quite a lot of extra clearance on the exhaust valve, about double what it's supposed to be.
 
Right now, the engine will start only if I block the throttle near an idle position.  The governor has it at full open with the engine not running, and it will absolutely not start in that position.  Once I get it running at idle, I can SLOWLY allow the throttle to open and the engine speed will come up and it will begin to regulate and run fine.  If I release the governor at idle, it shoves the throttle all the way open (because the engine speed is low) and that will kill the engine.
 
Any ideas?  This thing is kicking my butt!  I'm guessing a fuel issue at this point, it really seems like it should start at wide open throttle.  I may put the original carb back on and see if it really has the same issue too.
 
TIA,
Jim

Thanks Roy.  I may pursue the project in the spring, not sure.  I am able to start it if I hold the throttle at about 1/3 open, and then it runs fine. 
 
There was no saving the OEM coil.  The original coil had the small wires exiting the bottom of the coil behind the core, between the core and the body of the engine.  The replacement had the two small wires exiting in front of the core, between the core and the flywheel.  I had them tied back really well, but they must have been against the shaft of the flywheel.  There's just no way to make that work.  I considered rotating the coil 180 degrees, but then the wires seemed too short.  It's just not the right arrangement.  Funny that the aftermarket coil didn't have the same issue, maybe there is another OEM coil and I got the wrong one.
 
It does seem like I should be able to fix up the original carburetor, I'll give that a try in the spring.
 
Thanks for taking the time to help! -- Jim