In my search for ways to enable simple debugging when working in Eclipse with both FDT and FlexBuilder, I managed to find two viable options: Arthropod and LogWatcher.
Arthropod is an AIR application that enables enhanced logging for AIR, Flex and Flash applications. I am surprised there was not more fanfare made of this recently, as it was just released and got a mention on The Flash Blog. Arthropod allows you to use a simple bundled class to write trace statements to the running AIR application. This means, in theory, I could avoid having to switch back and forth to the Flash CS3 IDE to compile and debug with trace() statements. What I like most about Arthropod is how simple it is to use. Import one class, fire up the AIR application, and you are ready to go.
The second option I have come across is LogWatcher. I found this one on Josh Buhler's blog a while back, but never got around to installing it. LogWatcher is a bit more integrated into Eclipse/FDT, as it puts a panel in Eclipse that reads the continuous output of the debug Flash Player. You'll need to set the debug Flash Player to output all trace statements to a text file, but simple instructions can be found here.
Between the both of these options, it looks like I can finally stop having to switch to the Flash IDE to debug my projects.