Huh these places are reasonably far apart & you're going to be spending 3 days transiting just inside Europe to get to these 3 different islands / countries. How many weeks EXCLUDING arrival and departure days? Skip Gran Canaria, it's off the coast of N Africa & quite a ways from the other destinations.
Have you actually looked at flights? Use Google flights, search on destinations & prices may help you figure out where to go in what order. Make it a multi-city flights, so you can fly in to one place & out of the other. Make sure you're not there over May 1st , Labor day, & the weekend before or after, many many people have the entire week off.
Personally, i would focus on the absolute musts you've already identified, May should be OK for swimming in Sicily, I've swam May 1st in the Amalfi Coast but it wasn't warm. Sicily seems like a winner, lots to do, lots of beaches, use Search bar at top for more ideas, a very cursory glance found these - https://community.ricksteves.com/travel-forum/italy/favorite-sicilian-beach-town. Agreed with valadelphia, May is early for swimming, it's not going to be WARM, so if that's a must, maybe skip something (Spain?) and add Greece.
Ischia, Gran Canaria, Crete, or Cyprus. - Well, since you've mentioned Montepulciano, (WHY? To drink wine? Sample hilltop town in Tuscany?) which you can access from Rome but pretty sure there's not a train all the way to this hilltop town... so you'd probably rent a car (somewhere?? Perhaps from FCO), drive there & back & then take train to Ischia on a LONG day. (Others may suggest someplace closer to it to rent a car.) Ischia is probably the least touristy place you've mentioned. Good luck! Get back to us as you book flights, will be interesting to see how you route it!