I dont know what is on the bottom of the later Escorts transmissions. On my 2nd gens there isnt any drain plug & the filter is inside the oil pan on the bottom of the trans.
Its not too hard to pull off one of the rubber hoses connecting the trans cooler in the radiator to the transmission, and let fluid spray out with the engine idling. As long as you make the attempt to fill the trans back up again before driving around, it wont hurt anything.
The line from the transmission to the cooler in the radiator is the one emerging from the top of the transmission near the bell housing. The one bringing fluid back from the trans cooler is the one connected to the fitting on the front extreme drivers side of the trans. You would likely have to remove the air filter housing to see/reach it.
That would be the one I would pull off, and either connect to a similar sized tube, so as to run it into a 5 gallon bucket, or have the risk of ATF getting spattered all over.
I have not worked on a 3rd gen Escort. With the 2nd gen Escort automatics its difficult to reach some of the 19 small 6mm bolts (with 10mm hex heads), and they seem to get horsed up with cross-threading or stripped threads during reinstallation. I prefer to drop that front-to-rear crossmember to have direct access to dropping the oil pan. Some members have unbolt one or two motor mounts, jacked up the transmission a couple of inches, to make it easier to remove the oil pan, without damaging the small bolts.