What cocktails can I make with whiskey, lime, sweet tea, sweet vermouth, lemonade, and whiskey sour mix?

It sounds like you're looking for a cocktail that incorporates a variety of ingredients, including whiskey, lime, sweet tea, sweet vermouth, lemonade, and whiskey sour mix. Based on the options provided and matching them closely to your preferences, the New Orleans Ice Tea might be a great choice for you. While it doesn't specifically include vermouth or whiskey sour mix, it does blend elements of whiskey, lemon-lime soda, and iced tea, creating a refreshing and spirited drink that's close to what you’re looking for.

Another option to consider is the Lynchburg Lemonade, which also features whiskey and lemonade along with sour mix and triple sec, resulting in a sweet, tangy, and invigorating drink. Although it doesn't include lime, the combination of sour mix and triple sec should provide a delightful mix of citrus flavors that you're inclined towards.

Both cocktails offer a zesty, refreshing experience and balance the strong notes of whiskey with complementary sweet and sour flavors, aligning closely with the kinds of tastes and ingredients you enjoy.