..and Trento a lovely city, still with relatively low levels of tourism.
Rather than a group trip, I'd recommend seeking out situations that will likely put you in settings where locals or holidaying Italians are more likely to be encountered.
so yes, for starters, the further you are from the mass tourist trail the less likely you are to be presented with a menu in English, French, Spanish, German, Chinese etc. and indeed more likely to encounter a situation (as I recall in Rastignano, south of Bologna), where on asking for il menu, the waiter said "Non c'è - io sono il menu!", with me listening intently and translating for my partner.
Using apartment rental or agriturismi also helps, as although the latter do see overseas tourists on occasions, it's somewhat rare, with Italians a little more tuned into them. Conversely hotels are typically places where English is spoken as a matter of course.
When the agriturismo serves food, these are often convivial affairs, with locals often latching onto the nice setting and wonderful value food. Whilst these are often groups of people wanting to socialise together, they're still usually friendly enough for a brief chat. Those with shared kitchens open to residents offer an opportunity for easier conversations, and we had a lovely such evening in Cuneo, cooking and sharing porcini, and watching some Italina TV together.
Apartments get you interacting with specialist shopkeepers (or supermarket staff, but the food's less interesting there), and these are both a good way to reinforce the language, but also can bring some enjoyable conversations... plus it's a way of supporting the 'old ways' of specialists, over the blandness of supermarkets / hypermarkets (both in the vibe and the taste).
We like wine, and often arrange to visit wineries during the stay. Some speak English, others don't, and perhaps the most memorable was conducted in a spartan tasting room, with simple wooden table and chairs, with an elderly winemaker who spoke little to no English. A challenge for my language skills, but a very memorable / enjoyable experience. The chap is now a 'cavaliere' (knighted) for services to the local community, which might sit uncomfortably with someone who genuinely came across as quite humble.
Coming back to tours, you might find day trips through local tourist offices / independent local travel agencies useful. Away from the big tourist locations, these often attract a greater % of Italians. Likewise local events / festivals (away from the popular tourist-focused ones) are also much more appreciated by Italians (local or on holiday). The smaller the better. Finally, special interest groups e.g. walkers, knitters, mushroom hunters, board gamers etc. are also a wonderful way to connect with Italians, and whenever we've made such a connection, they've been exceptionally welcoming.
Good luck with this and as well as helping learn/practice the language, it will also embed you much more in the culture, and even the community. That can make it incredibly rewarding
