Just a couple of comments and questions. Regarding your numbered points.

#3 - That should happen immediately. Are you saying it doesn't?

#4 - If true, any suction would happen at the top of the panels near the VRV, not at the filter. It is the low pressure that opens the VRV but pressure at the filter should be higher because of the weight of the water? Is the equipment much higher than the pool?

Even if the VRV was very restrictive and only allowing a small amount of air into the system, it just means the water would slowly drain from the panels. That shouldn't allow an oscillation to be set up. My VRV is quite restrictive as well but I never experienced what you are. So I wouldn't expect that to be the issue.

Do you have a solar valve that shuts off when the pump shuts off?

Do you have air in the pump basket when running?

When the pump is running, is there air in the filter? This could be causing the oscillation.

Can you describe the solar setup in detail?

Height of the panels above equipment

Height of equipment above pool

Height and location of VRV

Pictures of equipment might help too.