There’s been several threads here on the subject of parametric rolling, some have dead links. Here’s the ABS document.
I still have a hard time wrapping my head around this. Here’s a graphic as a good starting point.
Fig 1 In the trough - high GM
Fig 2 -On the crest - Low GM
Your explanation is in line with my experience although it didn’t take place on the size vessel usually associated with this phenomenon.
The ship was a 600 geared Teu feeder vessel with very fine entrance and stern with a service speed of 17 knots. Built for European waters the sea conditions encountered in the Southern Ocean and Tasman Sea resulted in the distance between crests of the swells were close to the ships length. Consequently on a particular heading there was a constantly changing righting moment giving rise to an increase in the period and magnitude of the roll. This could only be alleviated by a marked change of heading.
Under new owners the ship broke down in the Sea of Japan and started synchronised rolling and foundered, without loss of life.