<p>I'm especially interested in memory profiling, reducing the size of a compiled .swf, measuring network latency, etc.  Also, I'm focussed entirely on AS3.</p>

FlexBuilder Pro definitely seems like a good option.  Downloading the trial now...
This article looks useful too:
http://flexblog.edchipman.ca/?p=7
I'm not actually concerned about measuring network latency, but I am concerned about measuring which parts of my app are slow because of latency, and which parts are slow because of boneheaded AS3.