Updated the initial post to include pictures. They're from my camera, so please excuse the quality. But from those, hopefully you can see how the waste pipe is situated in relation to the ceiling below.
Precisely, great drawing (be sure the top of the waste pipe is lower than the tub drain outlet). I couldn't think of a way to draw it and am too lazy to hook up the scanner.
It looks to me like you have enough room for a p-trap.Put it in line with the drain, run it into the side of a tee, drop down to an ell, and go into the back side of your pipe(ie. tighten the existing elbow 270 degrees or remove the old one and install a new one). On the top of the tee, install a piece of pipe to extend above the tub, then install a device called an Autovent. It will let air in, but won't let it out. I don't know the codes in Minn., but that would probably pass here and it should work fine.
I agree, you have space. I would probably cut off the plastic pipe coming out of the tub before the black fitting and cut the metal pipe to eliminate that elbow. Glue the trap to the plastic tub outlet and then connect to the metal pipe with plastic pipe plus a rubber coupling. A trap is only a few inches high vertically. You appear to have more than sufficient space if you eliminate some fittings you don't need. You may have to play around with some plastic pieces but it looks to me like it is very possible to do this right. You have a vent so if you do the trap right, this plumbing should be as trouble free as any plumbing ever is (i.e. not immune to hair plugs but no smells or other nonsense).
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