It sounds like you know your way around a water pump.
That plate people are seeing in the last picture is
not the cavitation plate. Your cavitation plate is under water in all three pictures, and the video. The plate people are referring to is the one I have circled in red. It can, and should be be well above the water line on plane. The plate circled in yellow is the cavitation plate. It should be right at the waters surface on a skiff like this on plane. The black spot with the green arrow is the water intake obviously.
Your outboard looks like it's mounted correctly from the information provided. Your cavitation plate is definitely at the surface or under water while on plane. In the video you can see the forward edge of the cavitaiton plate spraying water up over itself, the water trailing off the plate circled in red is being thrown up to it from the cavitation plate. Dropping the lower unit 5" with a bay kit would be the same as running a long shaft outboard on a short shaft boat. The extra drag from the wrong size shaft kills performance and affects handling, it can be so bad that certain hulls will not plane with the wrong shaft length installed.
It also looks like you have some sort of Doel Fin or other hydrofoil mounted to the cavitation plate. Those also create a lot of drag and can suck performance out, although that's not what you are trying to solve here. What I'm wondering is if the hydrofoil or it's mounting bolts are causing some sort of situation where it's creating turbulence and allowing air to be drawn into your water pump intake. Do you know if the pump runs dry without that fin? If not, take it off and see what happens.
If you can take a picture of the boat out of the water, everyone will be able to see how the outboard is mounted more clearly. A picture of a straight edge from the bottom of the hull to the cavitation plate would be good. Maybe a picture of the bottom of the hull as well. Something is obviously off here allowing air into your water pump, but I don't think it's how the outboard is mounted. You also need a new gasket on your outboard flush port
