I've seen this issue in two guitars recently.
One is also an Alvarez (of some vintage) that I replaced the "NB Ducer" elements with a Martin Thinline element a few years ago. Because fo the geometry of the original transducers, I filled the bottom of the saddle slot with a tight fitting rosewood strip (glued in place) and re-cut the slot using a jig of my own design (similar to the Stewmac but more precise, IMHO). The original saddle was trimmed to fit the new slot depth and edges lightly beveled. It was a snug fit and had good string balance when it left my shop. Unfortunately, the customer decided to sand the nut after reading some material online on how to improve his guitar tone. Needless to say - it came back but with the customer's financial state at the time, he needed an inexpensive, quick fix. The complaint was that "sometimes the treble strings are loud... other times it's the bass strings.
Fortunately, the bottom of the saddle and slot were still both flat. The issue turned out to be uneven pressure on the saddle and was resolved merely by tuning the strings from a slack state from the center to the edge of the fretboard (order: D-G-A-B-Low E-High E) on each string change. When the strings are at full tension, tuning order did not make any difference. I would have rather fabricated and refit a new saddle but he couldn't afford it. Ran into him a few weeks ago and confirms that the solution I provided him is still working.
Saw the same issue on a Martin DCPA5 (unaltered factory guitar, low mileage). Same string tuning technique worked on it as well.
The explanation of why this works is pretty simple. If you bring one of the E-strings to pitch with the others slack, the saddle is pushed down on one end. Intuitively, one might expect the bridge to move into an evenly balanced pressure state as the other strings are brought to pitch but this will not happen if the saddle is not properly fitted to the bridge.
Please note that I am not offereing this tuning technique as a suggested repair method but it is a usefull diagnostic aid to guage saddle to bridge fit and zero in on the problem.