In a large bowl, whisk together the Greek yogurt, Meyer lemon juice, red wine vinegar, garlic, paprika, cumin, cinnamon, oregano, salt, black pepper, and olive oil until smooth. Add the chicken thighs and turn to coat evenly. Cover with plastic wrap and marinate in the refrigerator for at least 2 hours, preferably overnight.

Position an oven rack in the top third of the oven and preheat the broiler on high for 10 minutes. Line a rimmed baking sheet with foil and place the marinated chicken thighs on it in a single layer. Broil for 10 minutes, until nicely charred at the edges. Flip the thighs with tongs and broil for another 10 minutes, until the internal temperature reaches 165°F. Rest the chicken on a cutting board for 10 minutes, then chop into rough bite-size pieces.

Rinse and pat dry the cucumbers and tomatoes. Trim off the ends, halve them lengthwise, and spoon out the watery seeds from both. Cut the vegetables into small cubes and place in a bowl. Add the thinly sliced red onion and toss to combine.

Lay a pita on a large piece of aluminum foil. Spoon a generous scoop of tzatziki down the center, spreading it slightly and leaving a 1-inch border at the bottom and sides. Top with the cucumber-tomato mixture and a portion of the chopped chicken.

Wrap the gyro by folding the bottom edge over the filling, then fold one side over while holding the bottom in place, and fold the other side over. Wrap the whole bundle tightly in the foil to hold everything together. Serve immediately and repeat with the remaining pitas.