If you decide to start moving drain lines under that slab, keep in mind that the septic line from the house is going to be pretty deep. Probably at least a foot below the bottom of the tub. (tub has to drain above the toilet, otherwise it would be a cesspool) Could turn into huge amount of digging, if you make any radical changes. Of course, it's just dirt and pipe and concrete, so it doesn't take a rocket surgeon to do it, but a strong back and stronger sense of purpose would be helpful.
Raising the tub to a normal height would be pretty straightforward, as pointed out, just by extending the drain.