If you put the hoses back after you got the air out, wouldn't you be putting new air into the system as soon as you unplug the line?

 

I thought the same thing but like I said, it worked for me... I'm thinking that once you have the big bubble out, opening the system doesn't do much if anything. The heater core is likely full of coolant now (after reversing) instead of half-full and not much comes out of the core when you open it back up. The hoses leak a little but the majority of the core is below the hoses so it should stay full. Of course you could just leave the hoses reversed. I didn't do that because they are different sizes and I didn't like the routing and stress on the hoses resulting from the re-routing. I hope that all makes sense.