After researching this and many other forums, we did the exact same thing: bought the Cosco Touriva. I very much endorse this as the best solution: the Touriva rates well, is small enough to fit the seats of the 737 even in the bulkhead, and it's a breeze to carry compared to others (it's the lightest in the Consumer Reports ratings). Plus, you can clip the tether on the back and use it as a shoulder starp to lug it around, without need for the bulk and additional weight of car seat carriers (a complete waste, IMHO).

Thanks FTers!