Depends on your child. DS only sleeps in two positions: lying down by himself, or in his car seat. He does fine in a CARES harness in lie-flats like the UA bed, so we dispense with the car seat for those flights. On the other hand, if he's in a reclining style seat, we keep the car seat and just recline it slightly by inserting pillows under the front of the base.
Regarding the UA 747, I'd book three seats in the first row of four in the middle of the downstairs cabin. Sucks for the fourth person in that row, but it will allow you to surround the child and give you a bulkhead in front of you instead of other people's seats.
And no lecture here. DS had been to five continents by the time he was 17 months old, all in premium cabins. IME, you'll find the dagger stares only really come out if 1) your kid screams, and 2) you are not obviously doing everything in your power to address it.