It's not only dimensions, though, weight is also a factor to consider. So even if you could theoretically cram a lot into a bag, even a lighter weight backpack, often you are given a restrictive weight limit that also includes your "personal" item.
Sometimes it depends on your fare class, too.
I just flew Air France and Lufthansa. For the AF flight to Europe it was a massive challenge to meet the weight restrictions using my heavy but size compliant wheeled international carry on. I also tried my 2 lb backpack, which eliminated 4 pounds, but was then so stuffed it was going to be a mess for the one night stays I mostly had plus, as you said, was heavy to carry. (With a 10 hour flight delay I was SO glad I took the wheeled option!)
In the end, I whittled down the items packed and was ready to pull out a couple of small heavy things for my coat pockets if the suitcase was weighed. I was just under the limit, but that was only accomplished with a scale, weighing each thing, Packing Forum support and all the angst. It's worth it to me to not check it!
On the way home, all on one Lufthansa ticket, I checked the carryon with my dirty clothes all the way through, despite it likely being the correct weight. Instead I took a very small zip-into-itself duffle to hold gifts purchased and a change of clothes.
Caveat: my previous Lufthansa inter-Europe flight, all passengers were required to gate check their carry on bag, despite meeting the size and weight requirements. And, despite all my preparation this time, AF never even looked at my bags! I don't know if there is ever a guarantee.
I did notice that smaller sized suitcases are sold in Europe and a Canadian on my trip had a suitcase somewhat smaller than mine. You might try searching for non US options?
I had your idea, too. And looked for a rolling set of wheels to attach to the backpack- who knew? They exist, but then they added weight that would've been over the limit. The pack sort of straps on to the pulling handle. But maybe?
Good luck!
