I remember worrying about the same problem with BA when we flew in 2015. I booked Business class with Avios, paid over $450pp in taxes/fees (one-way) because it was BA, and even that did not come with seat assignments. I ended up deciding as long as one of us was with DD it was ok with me, so I did not pay for seat assignments for DH, DD(10 at the time), and me - as it turned out we ended up all seated together anyway. We might have just been lucky, since if other passengers paid for a specific seat then they would obviously get it. We ended up in the last row of J class, middle section, those must have been the least desirable.
Do you have a credit card with an airline incidental credit that you could use to pay for seat selection (Amex Plat, Biz Plat, Gold, CSR, BoAPR, several others)?
As for earning in-flight miles in OneWorld, between BA and AA I prefer AA for a couple reasons.
1. I can easily transfer URs and MRs to BA, but not to AA. Thus I can access Avios easily, but not AA miles (I've gotten AA credit cards but I haven't done the graavy train).
2. I can book BA flights with sAAver miles (but pay the exorbitant taxes and fees - really only "worth" it for award tickets in J or F). I can only book AA flights with Avios if sAAver fares are available. I don't live near an AA hub, so that function is of limited use to me, since I would have to pay for 2+ legs and since BA is distance-based per leg, that might be more costly with Avios.