Since you have gone this long without international travel, suggesting it's a once in a lifetime thing for you, I would humbly suggest that 1) having booked the land portion for 5 people to one of the most expensive countries in the world it's pointless to worry about pinching pennies now, and 2) there is relatively little benefit to spending a great deal of time worrying about miles/points. In the time remaining a busy middle-aged person is highly unlikely to learn all the tricks and techniques to earn and then book enough miles to fly 5 people to Italy, so you are just creating a lot of work for yourself to perhaps little benefit.

Use Kayak, alerts services etc to help you shop on price, and simply buy the tickets you want for your party when the time comes.

It is not particularly important to economize on something you do once in a lifetime. If you save a few thousand dollars one time it's not going to change the lifestyle of a fiftysomething any.

The value of miles etc. comes when people make many and repeated trips, thus the savings adds up to hundreds of thousands of dollars over their lifetime. Also saving a few thousand dollars means a lot when you're a college student but it just gets lost in the noise when you're middle-aged.

I just don't see a complete noob starting from zero miles in all programs in their 50s getting enough miles together through various hustles to get five people in business class on award tickets in the time remaining to you. I'd be surprised if you could make it happen for coach tickets TBH. And considering the learning curve, for a one-time thing, if you're going to end up in coach anyway, seems you might as well save the time and just buy the tickets and have everyone end up on the same plane...

I don't know what you mean about "maximize the benefits" of buying the tickets. Each of you is going to earn, I dunno, say 10-12K miles apiece for your flights between North America and Italy. In other words, the miles you earn for one TATL trip will be of little value, which hardly matters since you don't normally travel internationally anyway so...it's another example of frequent flyer programs are actually supposed to be designed to provide the benefits to those who fly frequently, not those who fly once...so there's going to be nothing much to maximize really.

My vote is that once you committed to this trip, it may have been somewhat unwise to look backward and worry about money. I think it's about 90 percent guaranteed to be an expensive trip. Just think of all the money you've saved by never traveling before in all those decades and don't sweat it. You're still coming out way ahead.