True wheel but with high spoke tension variations causing pulsing brakes?

I bought a used powertap wheelset on ebay. I'm having an issue with extreme pulsing while braking, to the point of it being dangerous to ride in NYC traffic. The wheel appears laterally true to the eye, and the first two bikeshops refused to believe it was anything but old breaks, both replacing cabling, adjusting calipers, and cleaning the pads. This made no difference whatsoever.

The 3rd shop suggested that occasionally a wheel may have a manufacturing error that causes a defect in the brake track. These small variations can cause the brake to disengage and then regrab depending on where it's at on the wheel. The only fix suggested was a complete rebuild of the wheel with a new rim.

I did notice, however, that there is some pretty dramatic variation in spoke tension on the wheel despite it being laterally true. It is a bit out of true radially however. Just testing by ear, there was as much as a 4 - 6 whole note variation when plucked like a guitar string (within a single hub side) between spokes. There was much less variation on my other rear wheels, even one that's clearly out of true.

Is this normal? Could a wheel be 'true' but still badly tensioned? And if so, could this be causing the braking issue?

Any help would be greatly appreciated before I go spend a few hundred bucks to build a new wheel.