It's a bit hard to tell from the photo, but it sort of looks like there
might be a pretty heavy piece paralleling that cut joist just an inch or
so behind it.

Looks that way to me too. But it doesn't look like the cut joist has
much to hold it up except for the nails from the floor above. If thats
the case, I'd just cut the joist a 1.5 inches more on either side of
the pipe, then add two cross pieces from the adjacent joist to the
larger beam. These can support the cut joist, which will butt into
them. Use joist hangers on the cross pieces, installed before you put
them up, otherwise nailing near that pipe will be a pita.

-Kevin