2 inch p trap in 2x6 bay

I am putting in a tile shower in our attic space. I am putting in the drain but finding out the p trap isn't fitting into the 2x6 floor joist space. Is there any way to reduce the heighth of the trap without having to raise the whole subfloor to accomadate? Reason why I don't want to raise the floor is that our ceiling height is already tight with the angled ceilings.

The short answer is no.

I think were going to have to cut into the floor below and frame a box to allow for the couple inches needed.

trap

There may be ways to do it, but you would have to get together with your inspector to find out if he would allow them. I cannot go into details, because you might either misinterpret them and do them incorrectly, or not check with the inspector first and get into trouble. ALso, the possibilities depend entirely on the location of the drain line IN the joist space.