Still say its an intonation problem. Everything you've said points towards it.
1) Problem is only apparent with chords
All the notes (up the neck) are subtly out of tune, but you don't notice unless they're causing alternating constructive/destructive interference, as in with a power chord. If it were a problem with the pickup, it shouldn't discriminate between single notes and chords, and you'd hear an oscillation with single notes as well.
2) Problem becomes apparent as you move up the neck
The first few notes will be pretty close to perfectly in tune (hence no beats), but as you move up the neck it becomes more and more out of tune, hence, the beats become more apparent. Once again, if it were a problem with the pickups, there's no reason I can think of that it would only be apparent higher up the neck.
3) The sound "slowly oscillates" as if someone were moving the volume control up and down a bit.
The tones (and/or higher harmonics) are causing alternating constructive (gets louder) and destructive (gets quieter) interference due to their waveforms not matching. I'd guess the interference is going at a rate of between .1-10 cycles/second (ie it gets louder, then quieter, between once every couple seconds and ten times a second). I've heard plenty of problems with pickups in my time, but none that causes a constant alternation of volume, only with chords, that only becomes apparent as you move up the neck.
It's definitely a much more simple explanation than something being wrong with the pickups or amp, and as far as the guitar tech, 9/10 of the time they don't know what the hell they're talking about.