Factory recommended method
The factory service manual recommends a slightly different procedure. I don't have it in front of me so can't quote exactly. It does include dropping the pan but then you put in a few quarts of fresh fluid and pull a transmission cooling line from the radiator and run the engine to use the fresh fluid from the pan to pump out and replace the dirty fluid in the system. Once it stops flowing then the pan is empty. Shut it off, put the line back, and do the final fill with new fluid. I think it took 12-14 quarts total if I remember correctly.