As you note, the best way to reroute the drainpipes is to work from below. If you have an unfinished basement below your current bath, the job will be easy. It sounds like you have some sort of finished room below, since you mehtion opening up the ceiling. If that is the case, you will either have to open the ceiling or you can work from above by removing the floor in your bathroom.
If the joists runn parallel to the length of the tub, you will have plenty of room to lay out the new drain extension. If not you will have to notch or bore the joists to admit the new drain extension. The shower requires a 2″ drain, but you can get by with a 1 1/2″ drain for the tub. If you have to bore or notch up to 2″ holes in an 8-10″ joist, you should be OK, especially for a 3-4 foot run. For added strength you may want to sister the cut joists and add blocking on both sides of your cuts. The joists under a tub or shower should be sistered in any case to bear the extra weight.
You will need to pay attention to the slope of your drain extension (min. of 1/4″ per foot). With a 36″ extension you should be OK.
It is possible to build up the floor under a tub/shower if you have enough ceiling height in the bathroom, but this is not an ideal way to go. The extra height of the fixrures creates a clumsy step up. And when the entire bathroom floor is raised in this manner, it leads to a clumsy step up into the bathroom.