Yes, youngho, I was indeed thinking of Griesinger's work. Good call!
It's been a while since I read it, and I don't remember the exact reason he gave for the 90 degree phase shift (probably skimmed over the velocity vector discussion as the math would have intimidated me), but I did try his setup not too long ago.
You see, I was thinking of using two plate amps, one for each channel, specifically so that I could get that 90 degree phase difference that he recommended. Unfortunately for me, at that time there were exactly zero plate amps on the market that combined a 4th order crossover with a continuously-adjustable phase control. I was on the verge of contracting a production run of custom plate amps that incorporated both features - a considerable investment, but it would have given me a product that was unique, at least until someone else invested in a similar custom plate amp.
Anyway, before making the commitment, I figured I better find out just how important this 90 degree shift was. I borrowed two plate amps with continuous phase controls, along with 2nd order lowpass filters, but with symmetrical placement to either side of the listening position that would be okay at least for the purposes of my test.
Now my test wasn't a blind controlled test - it was just me. I wanted to see if I could hear the difference between in-phase, 90 degrees shift, and 180 degrees shift (left channel relative to right channel, in the deep bass only). I could hear a difference between in-phase and not, but I couldn't hear a difference between 90 and 180 degrees. So I concluded that the investment to replicate Griesinger's recommended setup wasn't necessary.
The rack-mount amplifier that I recently came across combines a 4th order lowpass filter with a continuously-adjustable phase control, so for the price of a second amp Griesinger's recommended phasing can be duplicated in a Swarm. Maybe one day I'll revisit that, and this time have someone else do the listening without knowing what changes I was making so that I could eliminate listener bias (although at the time, my hope was that the 90 degrees difference would be an audible improvement over 180 degrees because I thought it would be cool to offer such a unique product).
Duke