Updates:
I just got back from the dealer with the explorer. They replaced the TC and the problem was still there (still slipping). So they removed the valve body and realized that the TC clutch modulator was stuck and its sleeve worn.
They dislodged the valve, polished valve and bore, and now it locks fully.
They did not charge extra for the valve body job, but probably they shouldn't had changed the TC in the first place...
Anyways, it works and I'm happy. I end up paying $150 for the frst diagnostic at a local shop, $160 for the solenoid block, $100 for ATF and filter and $1,200 to the dealer for diagnostic, parts and repairs (total ~ $1,600).