If I understand what you're trying to do, you may (probably will) run into some resistance and/or large fees. I assume you booked your flights using United's "MileagePlus" frequent flyer points.
First, I do not see any non-toll-free numbers in the USA for United MileagePlus or anything remotely related. Everything points to toll-free numbers. That said, you can try calling any United Airlines airport ticket counter - they should be able to either transfer you directly to MileagePlus, or give you a non-toll-free number if any exists. Here's the non-toll-free phone number for Honolulu Airport (they ought to be in a good mood, right?): 808-241-6522. If that fails, call their corporate HQ in Chicago - they ought to be able to send you to the right place: 872-825-4000.
United's website lists four numbers in Italy for MileagePlus contacts, but none are open on weekends - I assume those is the same numbers you found. Here's the link to their MileagePlus contact numbers for Europe.
Assuming you are correct and there are indeed available award seats at the low ("saver") level, I believe the primary issue you will have (other than reaching them on a weekend) is going to be fees for making a change at this late date. Unless you have elite status, I believe the cost is going to be $125 per person.
If you are successful in calling, you may also get dinged with a fee for the privilege of speaking with a human (United says: Service charges for ticketing with a United representative in the United States and Canada are $25 by phone, $10 at a City Ticket Office and $50 in person at the airport. Ticketing charges may vary outside of the U.S. and Canada and based on MileagePlus status level.). I would ask them to waive that fee since you were unable to do it online (they should be willing to waive that).
A potentially more problematic issue may be if you booked a round-trip, and if they have a rule that prohibits or limits making changes to an award itinerary that has already begun (that is, if they consider this one itinerary there-and-back, and if they disallow/limit such changes). I don't t know their exact rule on this but have some vague recollection that some airlines do this. Just be prepared if they raise that.
My advice would be to try to make it work the way you want, but be prepared to stick to the original flights in case you run into a roadblock that you can't (or don't want to pay to) overcome.
Good luck. At least you're in Italy!