I wouldn't do it. There's a slump pan in the transmission and the new oil will mix with the old so you'd need a lot of new oil to flush out all the old oil as well as flush the contaminated oil out. You'll also want to check the screen for the oil pick-up which requires the pan be dropped.
Makes sense Jeff. By "screen" do you mean the filter? If so, I planned on replacing that at the same time anyway. I should have mentioned that in my initial post. So, if I drain the pan, replace the filter and then go through the steps I mentioned in my initial post, will what I mentioned work? If not, is there a preferred method of home flushing?
Here's the entire plan in order.
1. Jack up the Jeep and place jack stands under the rear axle tubes. One on each side.
2. Remove the drain plug in my trans pan and let the atf drain thoroughly.
3. Remove the pan and clean or replace the filter.
4. Re-install the filter and pan.
5. Add three quarts of atf to the pan.
6. Flush the system as described in my initial post until the fluid runs clear.