Carry-on?

I am not sure at all about this, but I thought the US leg of a trans-Atlantic flight on a single ticket meant the international baggage rules applied. Do you have two separate tickets?

What are the actual dimensions of your bag (or whatever it is)? I'm female and have no experience packing men's clothing, but:

That extra pair of shoes is bulky. Do you really need two pairs? The most I've ever taken is one pair of lace-up walking shoes (worn on plane) and a pair of crepe-soled sandals. Not a beach person, I very rarely wear the sandals and think I'll probably take no extra shoes on my next trip. If something catastrophic happens, I'll pick up another pair of shoes in Europe.

I assume your list excludes your flight-day wardrobe. Maybe ditch one of the pairs of slacks. I spent all summer in Europe with just 3 pairs of slacks (no shorts, skirts, or dresses) and mix-n-match tops. Well, also underwear. You do have the socks stuffed inside the shoes, don't you?

Here's Rick Steves packing list:
https://www.ricksteves.com/travel-tips/packing-light/ricks-packing-list

I'm assuming that the RS packing list is a carry-on list given his tour group preference of carry-on only. The RS Classic (backpack) Carry-on is rated at 2,500 ci. I'm surprised that your list of stuff doesn't fit a 2,745 ci bag. Are you packing heavy flannel or heavy wool pants and shirts? Wear/carry the bulky stuff (like fleece jackets).

The Eagle Creek Tarmac 22 Wheeled Carry-On (is that the one you mean) is listed at 22"x14"x9" or 2772 cu in. That's the outside dimensions. The 7¼# of suitcase must take up some volume.

But still, I take along 2 pr pants, 1 pr walking shorts, 4 golf style shirts, no shoes, 2 pr underwear, a sweater, and a bag with my computer charger and a plug adapter. Somewhat similar to what you say your take. When I returned from a recent trip, I measured the volume of what I packed and it was 1400 cu in, about half of the regulation capacity. Somehow, what you say you are taking doesn't agree with what I see.

It seems you are packing very inefficiently.

Utlize the space inside the bag between the telescoping handles. There should be three narrow areas. Use these for your running shoes and smaller items that can roll or fold easily-- bikinis, socks, etc. (And don't forget to stuff items inside the running shoes. ) I put items into a couple of tube cubes for this area.
Lewis and Clark and REI now both offer expandable long (tube) cubes.

Use the packing envelope for pants and dressier shirts. T-shirts and other shirts can be rolled and put into the compression cube. (Rolling takes up less space than folding in many cases.)

If the packing envelope isn't too thick, see if it will fit into the inside compartment of the Tarmac's lid. (The zippered mesh lid should close to keep it in place.)

If you do this, you should have extra space left over.

The weight limit allowd depends on the airline you're flying and the gate agent. Usually, they go by their airline and don't really care if it is a codeshare or not.

One last thing....never believe you can pack what the capacity claims. The way the test is done has nothing to do with clothing or normal items. The bag is literally filled with small pellets and then the volume of the pellets is measured in a tube.

I was curious about the bag you listed and learned that it is bigger and almost 2 pounds heavier than mine. Except for size, the two bags appear to be very similar, so I can't imagine what's making yours so much heavier. Perhaps it's a difference in the materials.

Assuming that you got the Tarmac 22, this is what the specs say on the Eagle Creek website:
Product Specs
CAPACITY: 2450 cu in | 40 L
EXPANDED: 2675 cu in | 44 L
WEIGHT: 7 lbs 4 oz | 3.3 kg
FABRIC: Bi-Tech™ | Bi-Tech™ Armor | 1260D Helix™ Ballistic
DIMENSIONS:14 x 22 x 9 in | 36 x 56 x 24 cm
EXPANDED: 14 x 22 x 11 in | 36 x 56 x 28 cm

I recently bought the Eagle Creek Load Warrior Wheeled Duffel 20. Its label says:
Capacity: 2200 cu in / 36L
Expanded: 2375 cu in / 39L
Weight: 5 lbs 8 oz / 2.5kg
Material: 4200 Helix Ripstop / 420D Helix Oxford / 1000D Helix Ballistic
Size: 14 x 20 x 8 in / 36 x 51 x 20.5 cm
Expanded: 14 x 20 x 10 in / 36 x 51 x 25.4 cm

That 20 inch (51 cm) measurement includes the wheels and handle. The bag is soft-sided except for the back. You have to take all those numbers, even from the manufacturer, with a pinch of salt, but they seem pretty accurate for my bag.

So I'm wondering how I could pack so much more into my smaller bag on a recent test packing. I did use compression cubes for almost everything. I did make use of the 3 spaces down the back, although I didn't unzip the liner like I normally do. I typically unzip the liner and put stuff in those spaces, partly to make the back totally flat and partly to make some paperwork more secure.

I'm a somewhat tall, plus-size person, so my clothes are not small. I usually do not roll them in a packing cube. They seem to take up more, not less, space rolled. I fold them. The test (a 2-week trip to TX) was the first time I used the compression cubes and they worked great. The test also showed me what I can and cannot take on my upcoming 6-week trip to the UK.

Remember that compression cubes take out the air, not the weight. I limit my main carry-on to 20 pounds total, about 9 kg. I can lift more than that over my head into the bins, but I don't want to! In terms of size and weight I'm good to go for British Airways with room to spare.

I looked at the Alitalia baggage info and it seems very restrictive - https://www.alitalia.com/en_us/fly-alitalia/baggage/hand-baggage.html. Be sure to check with them about whether or not you will be allowed to carry on the Tarmac. From what Seat Guru says - http://www.seatguru.com/airlines/Alitalia_Airlines/baggage.php - and Alitalia says, it doesn't sound like it.

I use a 20" rolling carryon and pack: 3 pr pants, 7 tops, 4 camis, one week's worth of underwear and socks, one sweater or wrap, one extra pair of shoes (unless you have very "easy feet", buying a pair in Europe and walking for miles in them without breaking them in can be a little uncomfortable), journal, a messenger bag, and several packs of tissues and snacks. I roll the clothing (except the pants). So far I have not had to check the carryon. (Everything else goes into a Civita daybag, which is my personal item.)

Is it the Eagle Creek Tarmac 22? Looking at the product on the manufacturer's website, the suitcase frame, handles, and wheel system look heavy (and appear to take up a lot of interior space). Your packing list is quite sparse, so I'm not sure what the issue is regarding ability to fit everything in the bag. Is it possible to return the bag and go for a different model? At that price point you could easily swing the Tom Bihn Aeronaut or the Red Oxx Air Boss and easily fit all of that into your lightweight bag and have room to spare.