We had a not totally dissimilar problem with a room in our house.

The contractor we hired sistered and nogged the existing joists, so they created a new floor level (slightly proud of the old joists) that was flat and level.

This video is similar to what we had done. https://youtu.be/5-Rvv06_A0k

Because every joist was doubled up, the floor was much stronger and then a new subfloor and glue down hardwood added. Because you have a long span, this may not be sufficient to address the sag.