Oooh, the cacio e pepe does look great! So creamy. I'll be flying this route later in December, definitely going for that. How was the mushrooms / sauce with the chicken?
Re: the gelato melting - I always ask for it to be served after, and often ask for the toppings on the side (bananas in this case - both because the fruit topping is generally warm and causes faster melting, and because sometimes they are just way too sweet). You could try that sometime, they've never had any problem serving it later for me.