I think you are on the right track.
Cutting out the strange looking tee and lowering is one way.
If you don't reuse the tee, there are other fittings that could be used too.
A plumber would have either a snap cutter or use a carbide sawzall blade to make his cuts.
Then it would be put back together with no-hub bands.
Most disposers work with an outlet of 19" on a 7" deep sink,
So dropping it to 16" would allow for a 10" deep sink.
You can go lower too.