Reducing the depth of the joists may not be your best option here. If they have sagged in the middle, then it would seem reasonable to me to sister new joists to the old to give a flat plane.

If the floor joists have sagged in an old house removing the subfloor and sistering new joists to the old ones can be a good solution. Adding stiffness to the framing is better than reducing stiffness. If you are not doing a large area and the plywood is sound you can use 2x4's turned on edge which are cut to follow the floor and create a flat top. We used to use a metal rail system and a router to trim the tops flat. Install the floor as you would over a sleeper system. It is still a lot of work