In the overhead? ...or under the seat?

If it's under the seat, does it stick out? 22" is pretty long...

If it does fit in the overhead on a feeder jet, taking almost 2 feet of an overhead bay must make you popular with other passengers...

I agree with the concept of a hard case for protection, but keep in mind that if the equipment is carried on, it never leaves your control. Very few of us carry laptops in hard cases (the gear isn't as much of an investment as the data inside it). The Pelican 1510 looks like a good option that I'll likely check out as getting the camera in and out for inspection is a pain, but I've never had a protection issue carrying gear on in my Kata bags. First, they're probably more rigid than you're picturing, and second the bit of flexibility that they do have can be the difference in fitting into a compartment or not.

I got the Porta Brace CS-DV3 for Sony EX1 at last year NAB.
It's little tight but perfect for travel by car or airplane.
Camera + AC adapter + extra batteries + about 10 memory cards + Light + wireless mic + manual & cables

The 1510 fits in every airline overhead bin, save maybe a turbo prop plane. I've personally tested. Sometimes it has to go parallel to the isle, but no big deal.

For carrying my gear on the plane I use Kata HB-207, which accommodates everything, including my 5DMkII and some lenses apart from the EX1r.
But this bag is big and uncomfortable for daily use, therefore I bring along another one with me: the Kata CC-193 which is suitable for the camera with batteries, audio recorder, mic, cards and even the new Sony shoulder mount for the EX1.

This bag will go inside my luggage and will be filled with things for the flight: ideal for protecting my hard drives. I always have a waterproof sack with me - recently it saved my equipment in a tropical storm.
I was tempted by the hard cases... but their weight would force me to business class, which I am not ready to pay for, so I gave it up.