<<Your comment about engine speed seems the most telling to me.  During
climb,
the tension on the push-pull tube is different than in level flight.  It is
easy to imagine that going in and out of resonance.  A simple test would be
to
take a bungee cord and pull at right angles on the tube at mid-span and see
if
the characteristics of the hum change.>>

One thing we low-tech auto engineering types do to find resonances in
structures is to just go around banging on things and noting the resonance
frequency.  When we find something that sounds (resonance at the same
frequency) like what we heard that's usually it.  A light rubber mallet
usually works.  For something like a pushrod tube a rap at the center will
excite the fundamental mode and a rap toward either end will excite higher
order modes.

Just a thought
Gary Casey