Restaurant Reservations

You can probably practice enough to reserve a table in Italian (just use Google translate) in the event that you get a non-English speaking person. I often walk by a place I am interested in and just do it in person, as my Italian (mostly my comprehension) is better in person than on the phone! In Puglia's small towns, this should be easy. If that is not logistically possible, perhaps you can ask your accommodations?

We have hotels make our restaurant reservations.

only have phone numbers

Try to send a message via whatsapp. When you don't often speak English, reading is easier than listening. And you can always paste and google translate a chat.

If they read messages without replying within a few hours, or if they don't read messages at all, I'd follow both above advices.

We also have our hotel make dinner reservations for us.

I have successfully used WhatsApp to make the reservations. There are some places that don't have a WhatsApp account and for those I call. I don't speak Italian, so I type my request into Google translate and read it when making reservations. Many of the places actually speak some English and it worked for me quite well this past month.