Well CRAP, should have left it alone.

Actually I'm trying to talk myself into going out there and pull the hoses and back blow everything out with water and compressed air.
This has always worked the best by far.

I start by disconnecting both top and bottom radiator hoses from the motor.
Then I wrap the garden hose and air blower nozzle together in a wet rag and stick those in the bottom hose nice and solid and let the water run for about 10 seconds and hit the air so it blows the water backwards through the tanks and tubes.
I hit it 3-4 times letting the water fill a little then hit it with air again. (you want them to mix so the air accelerates the water)
Then I swap to the thermostat inlet with the stat out and do the same with the block.
The air builds pressure behind the water and accelerates it way beyond the speed it normally runs through the system and all kinds of junk comes blasting out of the the water pump lower hose connection..

Generally I'll do this both directions a couple of times but ALWAYS backwards first through the radiator to first push anything back out of the narrow tubes instead of farther into them. (same with the heater core)
Direction through the block isn't near as important, but I like doing it both ways a couple times.

Obviously you have to be a little mindful of the air pressure you hit the radiator with but the block gets a full on blast at 80-100 lbs.