1996 Chevy Camaro Possible coolant leak

Ok, so a few weeks ago my car overheats. I figure nothing major. So I take it home to flush and refill the coolant. BTW it's a 96 Chevy Camaro z28 (350 LT1) I mention this because they are reverse flow. So I flush the system till the water runs clear, and go to fill it up with straight tap to check that it's ok before I add the antifreeze. So I let it warm to operating temp. (I have a 160 thermostat) and then check everything. Well I find water/coolant coming from my tailpipe, the radiators full, or seems so, and the engine is bone-dry. I took out the thermo to look down into the water pump and it's dry (the system was properly drained of air too). So I decide to try again, this time filling up the water pump first. I then fill the radiator, fill the overflow tank, and bleed the air only to be met with the same results. So now I'm thinking I may have a blown head gasket (it was burning coolant too; sweet smelling white smoke). However, I wouldn't think a blown head gasket would get bad enough for straight liquid coolant to make it out the exhaust pipe. Any ideas?