yeah, pulling the cooler line is a perfectly fine way for removing most of the pan fluid so you don't have to take a mercV bath. i wouldn't feel embarrassed at all by doing it that way. i do it like that every time, not everyone has a flush machine handy, and thats how they work anyway
i know when i swapped in my mk8 trans it was completely empty, and took almost exactly 12quarts. so if your just doing the line flush, converter drain, and pan drop their might still be a half quart or so in the valve body. 11 1/2 quarts maybe?
but yeah, just poor in 5 quarts, fire it up and shut it off, poor in 4 more, and then fill it really slow after its warmed up. it will take a while since filling through the check tube will make reading the stick difficult... got to let it settle for a few seconds every time you poor anything in >.>
that should completely cure the shudder unless the damage has been done. and since you seem to have been driving like this a while, you might want to cross your fingers and toes.
cooler is also a GREAT idea, pretty much every ford passenger car only runs a heat exchanger in the radiator which causes the trans to run extremely hot. i call em trans warmers...
somewhere around 200+ is what i usually see. its really should be somewhere around 170-180... supposedly for every 10 degrees over 180 you get you can cut your fluid life in half. seem to remember hearing that somewhere
and along those lines you can imagine even with syn mercV's 60000 life, running at what 210* all the time is like 7500 miles