did you clean the over flow tank and the hose to it, change the rad cap?
that sludge was most likely just dex sludge, the trans i bet is just a coincidence. if the trans fluid had just old tranny fluid in it, not coolant as well. and the level never dropped or raised on you.
dex sludge does stick inside good. i flushed my engine and rad, by taking out the t state, put the hose back on, then i pulled the lower hose off the water pump, drained the rad, then put that hose back on. then start the engine, put the garden hose in the rad, let it run till clear water comes out of the upper hose to the ground/bucket. put that hose back on, drive the car for a day or 2 with just water.
then dump it again, and top off with coolant.
my coolant is still green, but the rad cap does get some sludge on it still.