I know what you are going throu Trever.
Something like this can drive a guy nuts.

O.K. lets try to pinpoint the problem down.

Symtoms:
1. It is responsive with choke
2. when the throttle is quickly pushed down it will hesitate
3. New Plugs help only for a short time only
4. Vacuum reading is 6 to 15 (with choke)
5. Balls in the carb missing or maybe wrong size

The missing/hesitation you report sounds like ignition (points maybe but more like condenser to me)

But that`s not your main Problem

Let`s start with Vacuum - mormal is 17-20.
When you rev her up the reading goes down.
If it goes up you got the wrong port. You need manifold vaccum.

Low bud steady reading pints to:

A - Late timing
B - low compression
C - sticking throttle valve
D - carb or manifold vacuum leak

A - You say timing is correct. (Just to make sure try to twist the dizzy a bit in both directions and see if that helps. Maybe the clamp went loose.)Popping from the exhaust means unburned gas (no spark)

B - If you have full power with choke we can also forget this
C - I don`t think so, cause that`s eays to check and you had the carb out already.
D - our best bet so far.

A Vaccum leak would explain why you get better response with the choke. It would also explain the dark plugs, cause you are running way to rich with the choke.

Second best bet would be a carb problem that causes lean mixture and explain all the symptoms.

here is a link that tells you about different vaccum gauge readings: Vaccum Tuning


The easyest way would be to borrow an other carb and bolt it on. If not try the new rebuild kit and get that dammed ball out ther first. An for goodnes sake, do the most eaysest thing first: replace the condenser.

Good Luck, Frank