A backpack isn't a bad idea, but you should be aware that some of the larger bags, like the Osprey or the eBags Motherlode, are too large to count as a personal bag. GAs and FAs seem content to let bakpacks on, even when they are really large, but you can't count on that. Having said that, you get a lot more volume without the wheels. Have you thought about getting something like the Osprey or eBags and pairing it with a rolling computer case? That gives you a wheeled base for the soft bag and puts the laptops closer to the ground in the wheeled case.

I'd also recommend that you look at the sticky at the top of this forum, that offers detailed instructions for how to bundle pack. Personally, I'd wear the casual shoes and just pack the dress shoes. I'd also think really hard about whether I needed two computers for this trip or if one might be left behind.