No more FUELING around I'm MISSING summer

I know you guys are a lot smarter on this stuff than I, and I am at wits’ end on what I believe is an electrical or maybe a fuel issue.  The bike I have is a second hand build by Hillbilly Chopper in KY and I have yet to have it run well but was told it did at one time. It has a 2004 S & S 96 ci  with a stock carb and Spyke Super-Comp electronic ignition set up as single fire on separate coils.  As I shift through the gears, it gets to a point  where the engine starts missing and if I attempt to give it more fuel it almost feels as if the brakes are being applied. If I push it from this point it will often just quit as if it ran out of fuel. After a minute or so it will start, but will again die if I push it.  I will give you a list of things I have done with no improvement:

Disassembled the carb and did an ultrasonic clean and float adjustment. Jets were stock unless hand bored.

Removed petcock and filter and cleaned. Not much dirt in filter.

Replaced supply line to carb.

Insured fuel cape was vented.

Drained 5 gallon fuel tank through supply line which only took a few minutes. No water in fuel. Changed fuel.

Insured float bowl was full when bike died on one test by shutting fuel off when it died and then draining float bowl into measured container.

Adjusted timing.

Checked compression: 150 lb on each cylinder.

Checked grounds, all connections and ohmed out each line from ignition module to destination, checking for excess resistance or short to ground. Found bare spot on wire to front coil shorting on front cylinder and repaired. I thought I nailed it when I found that one. All connections to coils are tight and key switch has been jumpered out to check switch.

Replaced Autolite Revolution HT plugs and gapped. Plugs pass through Spyke manual compression releases.

Replaced plug wires.

Exhaust tips are black but it may be caused by misfiring.

Plugs tips are white to tan.

The only thought I have left is the Spyke Super-Comp electronic ignition, maybe damaged because of bare wire, but a little expensive to buy as a shot in the dark.  Any thoughts, guys?  

I hate carburetors & I hate cheap a$$ gasoline...for starters. If I can't keep cylinders running efficiently by turning throttle, overloading by way of gas or air, I look at mixture, if that is not problem I look at electricity. Remember some cheap ass bastard might have used too small of wiring to accept constant current. Other than that I don't know & its likely I don't know, like I say I hate carburetors. If I were simply looking for a more steady mixture supply, the suggestion I have is a diaphragm carb.