Travelling with an infant, you’d be better off minimising connections, and therefore the direct LAX-LHR service seems the best option.

If you cannot get availability on that service, bear in mind that BA also flies direct to London from “nearby-ish” SFO, SAN and LAS.

www.newclubworld.com does indeed have bassinets, and travelling with a baby allows you to pre-allocate bassinet seats for free.

As ever, more information on your second European/UK destination would help in trying to better inform your redemption strategy to maximise the benefit. Be aware that LHR-EDI is all one class, but you will have both Arrivals (landside) and Galleries Lounge (airside) access during your connection in London.

Be aware that as a consequence of the Chase Visa promo and the recent change to permit AAdvantage members to redeem miles transatlantically, availability West Coast – UK is pretty tight over the summer, so flexibility will be essential, as will planning this well in advance.