The method that you used ran the new fluid through the torque converter.
Back in the days......when one only needed to change the transmission fluid if they were doing something out of the ordinary....otherwise....it was fine for life.......they had drain plugs in the torque converter.
Now......when we MUST change the fluid regularly.....there is NO drain plug in the torque converter......so the only way to change the fluid in the whole transmission.....is to run fresh fluid through to flush it out.
I would use Mercon V for the next change.
If you want to get carried away (I am anal about this because I shelled out just over $2800 for a FORD remanufactured unit at about 100K...and don't want to do that again).......you could put 9 ounces of AutoRX in
www.auto-rx.com and drive for 1000 to 1500 miles.....and then change the fluid.
The idea being to clean the hydrolic part of each solenoid out......particularly that torque converter one....as it requires a pretty complete tear down of the transmission to get to.
No certainty that this will solve the problem.....if the parts are worn......then it will not "unwear" them.....but for $25 for the AutoRX....plus new fluid after the 1000 mile run.....it is worth a try versus tranny replacement.
One fluid that you might look into is Mobil 1 ATF....easy to find, and a good ATF.
It is now Mercon V rated.