Took apart the 8568B RF section front panel to get to the attenuator. Remarkably easy, actually, except that when I reassembled it I forgot to plug in the little plug that powers and controls the attenuator.
Cue unstacking the display and taking it down once again to open it up...I got my workout tonight!
Anyway, I took apart the attenuator and examined it for signs of a major power excursion and could find none. I think it may in fact just be worn out and the contacts are not making good contact with the tiny resistive pads. Perhaps one of the solenoids is weak. A +15 dBm signal is capacitively coupling approximately -61 dBm through the attenuator from 0-30 dBm attenuation, and correct amplitude from 40-70 dBm attenuation.
Since I have no way to repair such a precision device, I am definitely going to need a new attenuator.