Wow, seems like quite an ordeal. I hope for your sake the missing screen isn't clogging something as well. It sounds like the ATF is helping, so another treatment or so probably won' be a waste of time or money.
My dad had a customer bring their Ford Tempo with the 2.3L in with 30k miles on their oil. When I removed the drain plug nothing came out. I walked across the shop to get Dad and by the time we got back to the car the oil was hanging down about 2 inches. It was about the consistency of recently chewed bubble gum. In that case, we did 3.5 qts of ATF and 1 qt 5W-30, ran the car for 20 minutes or so, and drained it while still hot. We then put in 4.5 qts 5W-30 and a new filter and the car continued to run fine for several more years. Normally though Dad suggested 1 qt ATF in place of 1 qt oil, run the engine for 20 minutes at idle, drain, change the filter and refill with 4.5 or 5 qts oil. In your situation, 2 qts of ATF with a 7 qt system seems reasonable. I doubt you'd need to go 3 days if you drive 120 miles per day. I think if the ATF is going to do the trick, it will do it within 120 miles.