I think the very beginning of the barrel is called the locking lugs, correct? The part that the bolt rotates into.

How do you clean this area out? I try using Q-Tips and can only get certain areas of it scrubbed.

You're talking about the barrel extension, which threads onto the barrel and contains the locking lugs.

Get yourself a GI chamber brush, and some long Q-tips from Radio Shack.  Running hot faucet water thru it in the big utility sink is the trick, then blow it w/ a compressor or the wife's hair dryer.

Brownells sells special purpose swabs also:

Brownells cleaning stuff

I've seen something called a chamber mop or whatever, basically a cloth version of the GI chamber brush, should work nicely too.