Bogged down While In Gear And Sputtered During Acceleration

A trans./converter issue won't usually cause the vacuum to drop that low. If it's not bad points like Sireland said it sounds like it's running lean. The "coughing" is clear evidence that it's misfiring whether it's due to ignition or fuel system related.

Related to rebuilding a carb, I realize you said you cleaned the carb but I've ran into them before that got crap in them that wouldn't come out easy. You should have blown it out with air. That will usually dislodge any foreign material in it and clear it out.