Which order to apply room correction tools?

Gotta burn to learn.  

Millercarbon: upon re-reading this, I came across as a smart ass. Sorry.  Not my intention.  

You obviously have deep experience in these areas, and your advice about placement etc. was very helpful, and actionable.  I know what to do with that advice.  Your advice about listening, clapping your hands and listening, etc. is harder to turn into action.  What do I listen for?  What do I do when I hear things?  Any elaboration would be appreciated.  

Nekoaudio: if you get a chance to answer the two questions I posed to you above, I’d be most grateful.

@alanhuth I haven't used MSO myself but I believe it can be used on its own to determine the PEQ you should apply to the subwoofers. I would not apply any manual PEQ to the mains, and instead let Dirac take care of it. But you need to perform the subwoofer PEQ and time-alignment first, otherwise Dirac's 2-channel measurement and filtering won't work as well.

The time-alignment I am referring to is the same as what a surround sound receiver or processor typically does. It doesn't have anything to do with PEQ.

Imagine your subwoofer is located 100 feet away from your head, while your left speaker is located 10 feet away. If you play a continuous sine wave at your crossover point of 80Hz, you could adjust the phase of your subwoofer until there is no destructive interference. But when you played music, things would sound very wrong because sound from the subwoofer would arrive way too late compared to sound from your left speaker.

This problem will then present itself when performing the Dirac measurements, and consequently the computed filters will not really do what Dirac thinks they will do, and things will still sound wrong.

miniDSP has some articles about measuring the time differences between speakers:

• Measuring time delay for home theater with the UMIK-1 or UMIK-2 and REW
  
• Time-aligning speaker drivers with UMIK-1 and UMIK-2
  

I'm also assuming your left and right speakers are essentially identical distance from your head, so Dirac or REW will measure a very small difference between their impulse arrival times.