I think the carb stuff is a symptom, not the problem.
That was my first thought as well. An ishy intake valve on the rear cylinder would explain every symptom.

 

I have a '98 Heritage Softail Springer Anniversary Edition with about 9500 miles on the odometer so you can see that it sits much more than it is ridden.
A few years ago, I got it down of off the lift, installed a new battery and it started fairly easy (with a little shot of starting fluid) and it idled pretty good but it would NOT rev up.
I did about everything I could think of after removing, disassembling, reassembling and replacing the carb including plugs, new petcock, a/c element, intake seals, fresh fuel, fuel additive, etc.) with absolutely no positive results!

I took the carb off AGAIN! Tore it apart and checked every part, used carb cleaner and compressed air. Put it back on the bike and had the SOS!

I knew (or at least suspected) the carb but after having it apart TWICE with no success, I was at best "befuddled"!

I took a break and had a beer (or two) and took the carb off AGAIN--THIRD time!
I did the same breakdown, used the same carb cleaner and used the same compressed air nozzle then put it back on the engine and it RAN, IDLED and REV'd up like it did when it was new!

Be patient. Try cleaning your carb again and if that doesn't help, maybe having another person who has worked on carbs before take a look at it.

BTW, I had the Springer down in '17 and it's doing the same thing so I'm suspecting that it probably has something to do with the ethanol fuel we get around here, even though I had additives in the fuel.
This year, I will get it down and go through the carb again and I will drain and refill the tanks with non-ethanol fuel before I put it away again (after a few Sunday rides!).

 

Is the accelerator pump nozzle facing the right direction?
it should squirt right into the throat and not the other way.

 

Could you explain what you mean by putting a vacuum on the back side of the butterfly please? It has a CV carb on it. Thanks

 

Yes the accelerator pump is facing the right direction. I have also disabled the accelerator pump and road tested the bike and it still had the same symptom's.

 

I am going to remove the carb again and do a wet bench test on it, with gasoline. I will also do another air pressure test on the float needle. Thanks

 

I am suspecting that you might be right about the intake valve. I am just trying to eliminate all other possible things. Tearing down the motor is costly and time consuming. Thanks for your input.