Well, the thing in your DAW either uses a full band delay, or an allpass filter to do what it does.
The thing between the pickups isn't really caused by a delay the same way as combining two pickups. It's hard to describe in words, and I can't think of where to find you a picture of it from here at work.
If you imagine the various overtones as sine waves running down the length of the string from the bridge to wherever it's fretted (or the the nut) you'll have the fundamental moving the whole string up or down at the same time. Anywhere you try to pick it up along that length, you will find it moving the same direction.
The first harmonic will be going up for half of its length while going down for the other half. When fretting below the twelfth fret, you'll have the string moving the same direction over both pickups. The neck pickup usually sits right where the 24th fret should be, so if you fret the 12th, you actually get a null in that first harmonic at that pickup. The bridge will get some, but the neck will have nothing to contribute. Fret above the 12th, and the null moves to somewhere between the pickups, and you get the string moving opposite directions over each pickup.
Higher harmonics have more of these alternations between ups and downs, and it gets pretty complex pretty quick, and is complex enough in its application in play that I don't see any good point trying to "correct" it. The right way to avoid the phase cancellations is probably to just use one pickup.
If you draw out that thing I described, you'll also see the reason for the difference in sound between the pickups in general, especially if you draw the various harmonics "to scale" in the proportions that they set up across the string.
Edit -
Wait! I found a picture over at
Lollar Pickups site: