Place the artichoke hearts in a clean kitchen towel or several layers of paper towels and squeeze with your hands to remove as much liquid as possible, then roughly chop. Repeat with the spinach.
Heat a 10-inch cast iron skillet over high heat for 2 minutes. Add the olive oil followed by the chopped artichokes, and 1/2 teaspoon of the salt. Stir to combine, then press down with a large spoon or spatula and don't touch for 3 minutes. Then stir, press again, and cook until deeply browned, another 3 minutes.
Meanwhile, in a medium bowl, thoroughly combine the cream cheese, sour cream, mayonnaise, lemon juice, half the parmesan, half the feta, and half the garlic, and set aside.
Add the spinach to the artichoke mixture along with the remaining garlic, red pepper flakes and salt. Cook for 1 minute, stirring constantly. Add the wine and cook until the pan is almost dry.
Remove from the heat and move the spinach artichoke mixture into the bowl of the cream cheese mixture and stir to combine. Transfer to a 2-quart casserole dish and smooth the top with a spatula.
Set your oven or toaster oven to the broil setting with a rack in the upper third position. Broil for 3 minutes until the top is browned and bubbling. Serve warm with pita chips.