Wow, lots of half-truths, over-simplifications, and some flat out wrong info here (all from well-meaning folks, I have no doubt, no offense intended).
I don't have enough miles for a RT to Italy.
Are you sure about that? Frequent Flyer programs are quite complicated and a quick, casual read of how many miles one might need for a particular flight almost always produces the wrong answer. The programs are intentionally complicated - the airlines are working hard (some harder than others) to confuse you, obfuscate your options, and generally stick it to you. If you try booking an award flight naively thinking they are going to help you and make things straightforward, you would be very, very wrong.
How many miles do you have for your trip to Italy and back (from where?)? In what program(s)? It's entirely possible you have enough miles if you know how to use them. Note that the airlines have an incentive to fool you into thinking that you need 2X, 3X or more miles than you really need.
I've been given the opportunity to apply the miles/points to the cost and pay the difference.
Most airlines don't offer this option; a few do. If available, it might be a good option for you.
My main take-away is to NOT expect American to ever lower their price for a one-way ticket.
Hah! American Airlines works harder than any airline in the world (and goes to great lengths) to screw members of their Frequent Flyer program. That said, if you know their tricks you can sometimes make good use of their miles (although it's harder than most airlines).
Economy seats are not the best use of air miles, but if that is what you want then best to book your outbound trip soon as the Saver level seats on AA can disappear
True. The good seats (which are very limited) are usually snapped up as soon as they become bookable - 11 months in advance. If you're hoping for seats in May 2018 (to popular destinations), it's late to be booking - unless you get lucky. Maybe you're lucky.
On Delta, economy to Europe is 30,000 each way and Delta One is 200,000. By my thinking 7 coach one ways > 1 First Class with lay flat seat
No, no, no... Delta has gone to great lengths to stick it to their FF members, so far as to 1) HIDE the award redemption charts (they're no longer posted on their website, which make it easier to trick people), and 2) have gone to "dynamic award pricing" - they now say "the number of miles you will need is whatever we say it is today" (that number varies). But "DeltaOne" (business class) is NOT 200,000 miles each way (unless you're a complete fool). Prices for US to Europe on Delta in business class can be as low as 70,000 miles (I'm flying from Seattle to Amsterdam on Delta in "DeltaOne" in a few weeks for that price). Of course, if you're willing to give Delta 200,000 miles for that flight, they'll gladly take you, um, them.
We find that flying Business in a flatbed seat we sleep on the plane, arrive rested and do not lose a day ( or two) to jet lag and fatigue.
Amen to that! I have come to conclude that flying a good, roomy, comfortable lay-flat business class seat allows me to arrive feeling great, and makes my arrival day usable and enjoyable. OTOH getting crammed into miserable cheap coach seats, with bad connections and a horrible string of flights leaves me a physical wreck on arrival, requiring 2 days to recover from the trauma. Arriving rested, fresh and happy effectively buys me 2 extra days.
I don't think that Delta has business class anymore, at least not on the A-330. There is just Delta One then comfort coach then coach.
"DeltaOne" is their "business class". It's pretty good (certainly far better than coach!) although not exceptional.
Bottom line: as nice and helpful as people are here, if you are doing anything involving FF miles, this is a bad place to seek good info. Get over to Flyertalk.com for accurate info.
Good luck & have a great trip!