We recently evaluated a 500 HP 4 pole motor on a pump application. The motor is started with a soft starter. Upon examination of the bearings we discovered fluting inside both the variable frequency drive and opposite drive end bearings.
If it were shaft currents, especially on a pump, the fluting would be typically on the non-drive end only, excess shaft current would be drained through the apparatus attached to the drive end shaft. We would more likely suspect a vibration issue with the assembly while inactive. What is base condition for the pump? Is it on a stable foundation or is it mobile? If mobile, and transported you need to “lock” the shaft to avoid axial or radial motion.
PAM winding is still a feasible alternative to VFD where simply two or three discrete speeds are necessary without the need for servo-like control, mostly for high power applications as was mentioned above. Only several extra leads and contactors but no nasty harmonics, reduction of insulation life and no additional variable frequency drive that takes space & is not cheap to buy or maintain, might become obsolete and most likely will not last as long as the motor.
Note that some shaft couplers are insulating; and therefore, won’t drain shaft voltages.

However, all of the soft starters that I have used are line (mains) frequency phase angle modulating. Hence they act as three phase variacs (variable autotransformers). I have not run across any stray voltage problems with these units. However, some soft starters modulate only two of the three phases. I don’t know what this will cause.

Regarding VFD’s, three steps are needed to protect the motor: 1) High enough winding voltage withstand voltage (dielectric strength), 2) Adequate thermal capability to counter the extra (5% or so) winding heading due to the harmonics, and 3) protecting the bearings from developed stray voltage (grounding, bypassing or insulating).

A soft starter is in the circuit for so short a time, it is not likely that the fluting is coming from the drive. My logic is that fluting is a low current long time event. Bearing damage that could occur from the very short and very infrequent duration of starting would have to be a very high energy (for that short time), and would more likely be pitting.

In evaluating all possible sources:
There have been instances where the external current is coming from the plant piping. This would be eliminated by insulating the piping from the pump (if a flanged connection, use an insulative gasket [no metal fibers or rims], and plastic sleeves & washers for the bolt set).

Other motor related sources: the API motor specs say to insulate one end where the shaft voltage exceeds 500 mV. This can be done many ways, and usually done on the non drive end. (Have you measured the shaft voltage?)

I am not a big fan of shaft grounding brushes, and grounding the plant piping may not be enough. Brush contact is not reliable, and may not drain all the current (same for grounding the pipe).

Anecdotally: an electric utilitie had system grounding problems that elevated the potential of “ground” in a dairy. The path to lowest potential was through the cow to the milking machine to “ground”. Milk production went down, it took a while for the farmer to get the utility to check their system. Finally they did, fixed the transmission system grounding, and the problem disappeared.