I've done it several ways, with the bucket seat, with the Evenflo Triumph and without a carseat.
I've flown with him as a lapbaby, no carseat and no guaranteed seat, at 13 months old. He was hard to handle on the flight there, just bouncy but not too terrible, but I thought it was bad because I had no idea how much worse a toddler could be.

The way home, we had an extra seat by us and Russ stretched out and napped the whole way. Sweet angel.
Angel became a toddler. The Triumph, well, sucked. One flight, I measured that Russ had exactly five inches for his legs between the carseat and the reclined seat in front of him. Moving his legs meant his knees bumped the tray table. And yes, it's wide and cut into my space when planes are already small in space! I started booking him a seat at 16 months because I thought having the carseat would help. Well, maybe. For the first couple of flights after that. But he knew he could get out of it - all he had to do was poop and Mom would let him walk to the back of the plane and change him.
When he was 20-22 months old, travel became a nightmare. Our flight back from Disney, he sobbed and screamed until the flight attendant asked me to take him out and hold him. He never went back in for the rest of the flight so I ended up next to an oversized paid for carseat and a clingy toddler on me. At 22 months, we unbuckled the carseat and turned it to face me so at least his legs were touching me instead of the seat back in front of him. (That was the five inches flight.) Oh, how I longed for the days when my biggest worry was how long I could play bounce up/bounce down on my lap!
When he was two, I bit the bullet and checked his carseat. And...it made no difference. This flight, he wanted to sit on the floor and use the seat to play cars. Or unbuckle so he could get close enough to the tray table to play cars. Or just unbuckle and jump on the seat. Or unbuckle and try to reach the "call flight attendant" button. I was pretty much near tears by the end of that flight.
(I want to add, normally I'm a pretty good parent. I know it sounds like Russ is a hellion, but he's actually pretty good outside of an airplane environment. I think it's because his daddy flies planes and he thinks it's his God-given right to sit in the cockpit - it's the way he heads every time we get on a plane. And yes, I do the "right" things like bring plenty to do, new toys and old favorites, a DVD player, snacks, etc.)
I'm buying a smaller carseat - I do know I won't fly with the Triumph anymore - for our upcoming trip, and I booked Frontier just for the in-seat TVs. And I'm praying that it'll work.
So basically, I have no idea which will work for the OP. Every option sucks.
