Thanks for everyone's input!
Yes, it seems as if for some reason the pressure in the inner/outer wall chamber is oscillating. I notched the inner wall in three places at the bottom with a hole punch and I did put a bead of JB weld along the top of the inner wall when assembling to prevent any vapor leaks up there. I didn't bother with anything like that at the bottom since it is notched anyway. The design I used was the open jet stove on zenstoves.net and I pretty much did it straight up as the instructions state with the exception of adding the JB weld seal along the top (Pepsi-G stove suggests this).
I'm glad to hear this isn't that uncommon. If it doesn't effect the efficency it's probably no big deal. It sounds like from various sources it almost doesn't matter exactly how you burn your alcohol (open pan, open jet, closed jet, chimney, etc.) as long as you get the pot height and windscreen right.
Most of the time the breathing is pretty mild, but a few times the oscillations have been quite large - stove still kept itself lit though.
One theory I've got is that perhaps there aren't enough jet holes and pressure builds so high that vapor manages to force its way back through the notches at the bottom into the central chamber and thus vents the outer chamber and the pressure plummets. Then more fuel vaporizes and the cycle continues. A poor analogy would be the way a nearly full 2 liter bottle glugs when you pour it as air rushing in and liquid pouring out compete and set up an oscillation. Current design has 24 holes made with #74 drill bit - maybe I'll make one with 32 and see if there is a difference (Pepsi-G uses 32). Another difference with Pepsi-G is the notch sizes - and Pepsi-G specifies different notches for different types of cans so maybe that's related.
Was cool to boil a pot of water in my sink with the little stove anyway!
Any other ideas or suggestions greatly appreciated!