raise P trap ??
ok, now a dumb question from me: why does the tub's existing P trap have to be so low as to end up 8" below the ceiling of the basement? I thought the P trap could be higher. The higher it is, the higher the tailpiece pipe coming out and going to the stack.
By the way, that pipe is and remains horizontal (with 1/4" /ft slope) whether it is straight or with an elbow. Not slanted up, not sloped upwards. Slightly sloped downhill, not less than 1/6" per foot, ideally 1/4" per foot. ((If slanted too steeply, it requires a vent near the P trap; depending on the distance to the stack. This is hypothetical information only, as no-one ever installs it this way)).
So far you have not mentioned venting. This is serious.
If you place the P trap so high up in the space between two joists that the tailpiece is now too high to pass under the joists, you have to drill holes in joists to keep that pipe horizontal (with 1/4" /ft slope). Can be done, has been done, not a new thing, not against code. If you really want to, you can do it. Is something preventing you, which I am not aware of? It is best to keep the same trajectory, same path, instead of lengthening it, in my opinion so far. If you go on the path you mentioned in your first post, with a 1/4 turn elbow, you will have increased the total length of pipe from about 5' to 7' or more. Then you may have another problem because this increased distance to the stack may then cause a requirement for another vent, regardless of slope. Is the tub pipe 2" or 1.5" diameter inside?
david