I think that the Aviator bags do not have cart straps. You would need a way to keep them on a cart. I've traveled that way with an Air Boss and still had to stop and adjust the load a few times. And an Air Boss has more structure than an Aviator bag.
My cart is a small folding one and is still a hassle. Essentially if I left enough room to pack it, my bag would be light enough that I wouldn't need it. I ended up carrying it on.
I think tfar has it; just use an airport cart or ask a porter to assist. But if you're sold on having your own cart, look at the Wesco folding ones. The mini mover is rated at 110 lbs. There is a heavier one called the maxi mover. In your case you would probably have room in a large aviator duffel for a mini mover. I would likely just check it. They're pretty tough. Check their site or Amazon before you buy. If you're on a tight budget there are copycat models of the mini mover for as low as $30... Half of the cost of a mini mover.