I'm not sure knowing the make and year of the engine makes any difference on this. Typically, a blown head gasket either allows water into the crankcase (if the leak is between the water jacket and the oil passage) and your oil will look like a chocolate milkshake or you will see steam (white smoke) if the leak is between the water jacket into the cylinder. Also a leak into the cylinder has a tendency to pressurize the coolant such that the coolant in the radiator seems like it is boiling.
I'm not sure how coolant reacts with xmission fluid, but I do know if you run your tranny with a large quantity of water in the fluid you'll be looking at a rebuild. I would start by looking at both the engine and tranny dipsticks for abnormal color and/or levels. Another thought may be two different types of coolant were mixed together that were not compatible or possibly not diluted properly with demineralize water (although I've never seen improper dilution result in the solidification of the coolant).
Please keep us informed in what you find and good luck.
Lou
05 Travel Supreme Envoy