How can I connect floating 2x6 wall plates to 4x4 posts?
You could add PT 2x4 to each side of the 4x4 post cut to the length between your 2x6 top/bottom trim boards, then screw your 2x6s into the end-grain of the 2x4s.
This would give you a 90° screw connection, but honestly, toe-screwing them in (from the bottom side so water doesn't collect in the holes) would probably be sufficient. If you're feeling fancy, you could even use a pocket-hole jig and screws to make nice neat holes in the 2x6.
Considering that people use pocket-holes/screws for assembling cabinetry that can hold 100s of pounds (I've got a tool rack in the garage that's pocket-screw assembled), that should be sufficient for your purposes.
As a side note: You may consider leaving a bit of a gap between your 1x8 PVC trim to allow wind to blow through a little easier. I doubt you'll have issues, but being in a coastal region, wind is an issue, and a bit of a gap will make it easier on the whole structure.