Alright...Let's see if I got this right. I'm a little confused as to what order I should be doing things in.
1.) Flush tranny.
2.) Disconnect return/send hose from radiator to tranny. Flush radiator to get as much pink milkshake out of the block.
3.) Put new radiator in. Fill w/ new coolant, of course.
4.) Put new tranny filter in and replace pan.
5.) Run and flush tranny a couple of times.
Do I have that right?
Almost, the problem is it's hard on the tranny to flush the cooling system and vise-versa with all that milkshake in there. You may want to do a machine power flush on the cooling system so the engine doesn't have to be running (as opposed to a garden hose in the inlet). Flush the cooling system with the bad tranny cooler plugged off from the outside. Then replace the radiator and leave the tranny send line off.
Then...
1) Drop the pan/replace the filter.
2) Fill with ~4 qts of cheap ATF
3) Put the send hose in a bucket (the return hose from the radiator can be hooked up)
4) Start engine (now that the cooling system is clean) and drain 1-2 qts and turn it off. It easy if you make a graduated bucket so you can keep track of exactly how much you drained so you can refill the same amount. The tranny pump will shoot out about 1 qt. every 10-15 seconds or so IIRC.\
5) When it comes out clean (probably after 16-20 qts), hook the send line back up to the new radiator/tranny cooler.
6) Check the level of the ATF with the engine running, in P, after cycling through all the gears. Make sure it's at the cold level and not at the hot. Take it for a 20-30 minute drive and recheck the same way and it should be at the hot.
7) Check the fluid several times over the next few days. As much as it sucks, I would probably drop the pan one more time and clean the new filter because it will probably catch some crap that wasn't flushed out.
The write-up I linked to tells you everything you need to know. How to clean the filter, everything. If you plan on dropping the pan twice or even 3xs if necessary, use molded cork or rubber gaskets first and then FIPG the final time. It will make it a lot easier to drop the pan the next time.