I see alot of people interpreting the air gap in different ways and if you plan it into the build then its clean and no one can tell its there.
I never took a picture of mine so I made it a special point to share this picture.
Yes, you are right on track, if the stack is too long, the air column has a chance to cool reducing the pressure differential and slowing down the draft. According to the calculator, a 6" pipe three feet long would be just right. It should be an easy fix with your fabrication skills!
Sorry you are having a setback, everything else looks so great!
I would probably go with a 6" if it were mine. A tank that large needs to be able exhaust a lot of heat and smoke freely. There is a local guy who makes pits (real good pits) I won't say who but if you have watched Pitmaster's you have seen a couple of his pits on occasion any way his most popular smoker is the 250 gal. he has always uses 6" ID pip for his stacks, these things work great, flow great and hold temp like they should. Also I wrote Dr Blonder who is an expert in these things agrees that a larger dia stack works better on a smoker rather than a long small dia. Sometimes it's a little trial and error. Sounds like you are on the right track.