Don't forget to flush out your block - that chocolate milk shake is throughout your entire coolant system - I would also run straight water at first, get it hot and drain the system again before finally filling it with 50/50
make sure to drain the torque converter also. it should have a drain plug in it. i really dont know how much the coolant will effect the trans. need to talk to a transmission shop on how much you need to try to flush it out.
There is a flush machine that I am sure trans shops should have that will flush the entire system. When I worked at Pep Boys they had one. I say it would be best to locate who has such a machine and have it towed there. You don't want to connect the new radiator to it before the flush. MAtter of fact, the machine is connected at those connections so they should be able to hook it back together when done flushing.
the best thing you can use to clean cooling sys. is dish washing soap ( for your dish washer ) drain cooling sys. as best you can refill with water and soap and repeat and repeat and so on until clean.