My guess is that the vibration goes up when the pump is operating at low flow or well below the BEP operating point. The main evidence is the increase at 10 X shaft speed which is probably from suction pulsation frequency and the appearance of Cavitation based on the high frequency vibrations shown on page 15 of your report. The increase in vibration at 1X shaft speed may be related to excessive clearance in the radial bearing or less damping from the thrust bearing. If the pump housing or NDE bearing housing has a natural frequency close to 1X shaft speed, as you say, then the suction or discharge piping supports may change the natural frequency at different flow rates. I have seen this problem on a booster pump on a large BFP. I found broken pipe supports and a support that had hard contact that was supposed to be floating.
Actions: check flow rate and valve position, inspect pipes and supports at different flow conditions, and check bearing clearance during normal shutdown.