Is this something that has just recently started to occur?
Have you done any recent reconfigurations in your shack with the equipment layout?
Maybe take the cover off the P3 and see if slightly touching or moving the flat ribbon cable makes any differences.
I know Elecraft had provided a sticky-back clip to help hold that ribbon cable flat and in place snug against the sidewall of the P3's cabinet.
Interesting to note your noted noise level is quite consistent and/or precise with the band changes.
73 - Nolan K.