I did a lot of things with my twins, and was not easily put off trying anything, but your trip sounds difficult to me.
Whenever we flew with our pre-walking babies, we had to be super organised. There is often only one spare oxygen mask per row on the plane, so DH and I were normally in different rows, which means you have to cope with 'your' twin pretty much single handedly from boarding. Since you can't leave baby on your seat (because its not next to your DH, or in tour case because there is no DH), you have to take your baby with you if you need the loo , and then there is nowhere in the loo to put the baby down except a high changing space behind and above the loo so you have to manage the loo in a small space while holding a baby. Getting things out of the overhead locker is also difficult, but easier to get someone to help!
Having said all of that, you may be able to pay the airline to provide some sort of assistance. If you could afford a more expensive airline/first class you'd have some space, and you may be able to secure a promise of air steward assistance. I would arrange this in advance though. You would also have to be absolutely certain they would bring the buggy to the door of the plane in landing too - often we've been able to use the buggy right up until boarding, but then the buggies are sent straight to the carousel for collecting
. IME it tends to be the big airports like Heathrow/Gatwick that do this, while airport where you disembark down steps into the tarmac they'll put the buggies at the bottom of the steps for collection.
The airport bit of your journey sounds less scary than the flight to me. I would take a double umbrella fold buggy and find a way to attach the inflight car seat to it (strap it to a buggy board? Board would then stay on buggy for loading into hold?) Hand luggage would then be a rucksack. You could manage independently if you took main luggage in a large rucksack on your back, hand luggage rucksack on your front, car seat on buggy board, babies in umbrella fold buggy, but it would be difficult and you would need to allow tons and tons and tons of time. TBH despite my try-anything-once attitude, I don't think I could have done that with 4 month olds - maybe by 1 yr, when babies can be soothed for a minute by talking, needs can be anticipated a bit more etc. But that's just the airport bit - the flight would be logistically too hard for me I think.
I don't like admitting that its too hard to do something with two babies that can be done with one, but I think this one would have me beaten. Sorry.