There's no priority access lanes at the connections security. Sometimes it is indeed quicker to go outside and go through security there. However, generally I find the connection security to be pretty quick.
The process as you've explained it is correct, though there is no longer a customs check after baggage claim. You can walk straight out. (Some passengers are selected for an extra customs check, though.)
Feel free to check the MIA connection thread:
https://www.flyertalk.com/forum/amer...onnection.html