Eddie,

The goal depends on the issue - if there is one.

Breaking up a surface helps to avoid reflections of waves all heading in the same direction - but there are limitations to this depending on wavelength. With egg cartons, the surface will only do this for wavelengths shorter than the depth of the egg carton to perhaps slightly longer.

(runs to the fridge with a ruler....now he's back) The paper carton in my fridge has a depth of about 30mm, or a full wavelength of about 114 Hz or so.

They aren't going to add a huge amount of absorption to the space.

With the pictures that you showed of your studio space - I don't believe that this is your main issue. You have some really nice unintentional 'features' in that space - the sloping ceiling (blessing and a curse), the nooks for the guitars and fridge/microwave.

If it were me, I wouldn't waste the time with the egg carton. I would do some re-thinking of where you have things in the room. The monitor speakers MUST be moved away from the wall/ceiling corners. That's a key. Putting egg cartons on that sloping ceiling won't help that much there.

Go to the http://www.foambymail.com/AW2/acoustical-2-wedge-foam.html website and you'll see that 2" foam is quite a bit more affordable than what you post above. 48 square feet of it costs $62. That will absorb WAY better than the paper eggcrate and look nicer as well. 3" wedge foam is $87 for 48 square feet. And it will work for absorption WAY WAY better than the eggcrate; all for the same amount of elbow grease as hanging the eggcrate.

I would start with that one side of the sloping ceiling and anywhere you might get direct reflections from acoustic sources back into a microphone.

It's always good to have non-parallel walls, and broken up surfaces - lot's of folks use bookshelves with staggered depth books for this kind of a thing - but your room doesn't appear to be plagued with the 4 parallel walls and parallel ceiling/floor issue.

I wouldn't bother with the eggcrate if it was me. Quite a bit of hassle for likely minimal return in your particular room; again, based on what I saw with the photos.

-Scott