Bathtub drain trap too deep for new ceiling

I recently removed the original ceiling and two later ceilings in the kitchen of my house. A bathtub was installed around the 1950s above the kitchen. Two years ago a plumber came to fix a leak in the trap of the bathtub. He discovered a significant flaw in the design of the drain pipe of the bathtub. Basically, the pipe was level or slightly angled up between the trap and where the pipe enters the stack. His solution was to lengthen the trap of the bathtub drain and the trap now extends 5 inches below the joist. After the trap, the underside of the pipe currently is 4.5 inches above the joist. The pipe runs 6 feet to the wall, makes a right turn and passes through two holes cut in the top of the joists (hence the limit on changes to the angle of the drain pipe) before entering the stack.
I plan on having a new drywall ceiling put in at the height of the original ceiling (~3/4 inch below the joist) and need to find a solution to the trap of the bathtub that does not extend below the bottom of the joist. Any suggestions? Why would an extra deep trap help the flow of water out of the bathtub? By the way, this drain is not vented.
Thanks!