That is really odd. The neutral safety is inside the transmission and only "talks" to the transmission control module to allow the starter to engage when requested by the ignition switch so I don't think the starter is involved.

Has the car made any similar noises while driving down the road or any soft of random rapid "feels like a stick in bicycle spokes"?

This car should have a 5 speed electronic shift 722.6. There is a bushing between the input and output shafts that wears out, this allows the shafts to move radially to each other. This in turn overloads a needle thrust bearing causing it's cage to wear out and needle bearings to fall out. . . into the planetary causing gears to be jammed. I recently took apart a core unit with this issue.

I'd stop driving and pull the pan right away then look for 1/8" diameter x 1/4" long steel rollers and some bits of sheet metal from the cage. The pan has a drain, the gasket is reusable and you can use a paint strainer to filter the fluid and dump it back in if nothing is found.

I've pulled the pan on a few a few high mile 722.6 that apparently never had a fluid change ( the filter molding date was prior to the trans build date. ) and there was zero material in the pan save for a slight evenly deposited film.