Any suction near the VRV will produce a lower pressure at the filter.
I disagree. As I stated before, the VRV is much higher than the filter so the water above the filter will create higher pressure at the filter than at the VRV. This is static head. At the instant the pump shuts off and right before the VRV opens, the pressure at the VRV is ~ -6.5 PSI and the pressure at the filter is ~ +3.5 PSI (pool level is 0 PSI). As air enters the VRV and the water drains, the pressure at the head of the water is related to the height of the water.

Probably. When the pump starts, there is air in the panels, and it is forced into the filter. Eventually it all flows out into the pool and bubbles away, but there could still be air in the filter housing in many cases, and you are right that this could cause the oscillation.
The panels are plumbed after the filter so air should not be forced backwards into the filter. When priming, all air in the panels should be forced out of the panel return and then go forwards out the pool returns. Do you have a filter air purge valve? When the pump is running and when you open it, does air come out?

Also, when the equipment pad is well below the pool level, it is a good idea to install the solar valve and check valve on the side of the house above pool level instead of at the pad. Unless that is they way it is done now, that could help. The pad water pressure being higher than atmospheric could be causing an issue with the draining water. But that is the only thing I can think of causing the issue unless the filter accumulates air when the pump is running.