I didn't worry about timing it for naptime, but it always worked out that he'd fall asleep on the plane no matter what time it was.
Def get him his own seat, even if you don't take the car seat. We just buckled him into the seat like a regular person and for some reason, that kept him from thinking about getting up. He had a lot of fun tinkering with the seatbelt too.
We always checked the car seat. I know bringing it on the plane is best safety-wise, but I was always traveling alone and physically could not bring one more thing on the plane. You can buy car seat travel bags that have a shoulder strap or just make the straps really loose and wear it as a backpack (if you're bringing it on the plane). Take the smallest, most lightweight stroller you have, like an umbrella stroller. You'll have to pass it through the xray machine. You can take it all the way to the gate and check it there, it will be waiting for you when you get off the plane.
If you don't have a portable DVD player, def rent one. Saved our lives on many a flight. Make sure you have plenty of snacks.
I never got up with him once he was mobile. I was always afraid he'd refuse to sit back down.
Another tip...let him run around the airport like a banshee before you board. Excess energy on a plane is not a good thing. Don't board early unless you REALLY have to. The less time you spend confined in one place, the better. Like Emma said, try to keep your stress level down as much as you can. Even if he screams and throws a tantrum the whole time, you'll never see any of those people again!