You will probably be fine. I would say you almost certainly won't have anyone checking at the gate in the US - and you will be ok finding space in World Traveller Plus overhead lockers for your bags too, which is the issue.

You will probably be fine in London, too. The absolute worst case scenario is that they gate check one of your bags for you in London. Obviously they won't charge you to do this.

If your bag really is oversize then try to avoid lingering around the gate area before boarding starts - by the time boarding has started, the ground staff wil be busy actually dealing with boarding so will probably avoid gate checking your bag if they can help it.

I'm an exception to most people and I really HATE to carry everything on - I like to check my bag in and not have to worry about fitting it in the overhead locker. As I don't have particularly sharp elbows, I invariably find that by the time I get to my seat, all of the usable space is gone and then I have to try to shuffle down the aisle to find somewhere to put it, and then shuffle back to my seat ("sorry, excuse me please, sorry, sorry, sorry, excuse me please..."), which is disruptive. Of course, a lot of people spring up before the aircraft is on stand so I then have to wait until most other passengers have disembarked to go and retrieve my bag as I refuse to move until the seatbelt sign is off. But that's just me