A 1-1/2" trap arm can go 42"
2" trap arm can go five feet
A 3" trap arm can go six feet from the vent.
Some areas allow for a wet vented fixture over a tub drain, so if you have a lav nearby, you could possibly use that as a "wet vent" for the tub. That may get you your six feet.
Keep in mind though, your plumber has seen your home, we haven't.