The pre-edit stereo track sounds and looks in phase to me - the (+) peaks on the L channel match the (+) peaks on the right channel. Same for the (-) peaks on each channel. As you suggest, there's a clear dlineation at the ~19s mark when you switch to dual mono. However, I then hear mono through the rest of the sample - including the click around the 22s, which seems odd. It ought not be there, yet...there it is. Something screwy is going on at that point. When does the dual-mono edit end within the sample? Even if it ends at that 22s mark, it ought to be a cleaner transition, without the click, a la the cleaner transition from stere to dual-mono at the 19s mark.
I'm guessing what you're hearing as "going back in phase" at the 19s edit point is simply the complete removal of time delay differences due to switching from a stereo signal to a dual mono signal. A dual mono signal sounds inherently "cleaner" and more in-phase because there are absolutely zero time differences across the L and R tracks since their source is the exactly same. In the pre-edit stereo signal, there's a slight delay between L and R channels, even though they're not out of phase, which contributes to the stereo image - perfectly normal and natural sounding, I think. This is a Good Thing, IMO...else we'd always record in dual mono.
But something screwy is happening at the 22s mark, with the click, and I'm not sure what. Are you trying to switch back to stereo at that poing? If so, it doesn't sound like it's happening. It still sounds dual-mono to my ears. Re-trace your steps as you suggested and confirm you're switching from stereo to dual-mono and back when and as you wish?