I've always had gyros made from ground loafs that spin on a hot vertical rotisserie. I didn't know that whole meat cuts would be considered a gyro at all. All those spices mixed into the lamb loaf is what makes it a gyro to me, and it all holds together just as if it is one piece of meat and not ground.
By the way, are french fries REALLY a traditional addition to a gyro? I've never ever ever seen them used as a filling or topping. Always served on the side if they come with the order. Seems strange to me that it's a "traditional" topping in Greece. Seems like an American hamburger throwback if anything.
Weber Spirit E-310, Weber Performer, Weber Smokey Joe, Mini-WSM, ECB Electric.