Please note that the base plate on your newer style bridge is thicker than on the classic older style bent metal Fender bridges.
This is absolutely true, I meant to mention it myself, and it can limit how low you can set your action.
Again, if all other factors have been addressed and you still can't get that action down without bottoming out, a shim will probably be your only choice if you want to keep that bridge plate.
I have switched out those thick bridge plates for the standard Fender Bent-L bridge plate, which is thinner.