AA has an official policy in this area, US a semi-official policy. IB and BA do not have this policy, and linking doesn't get this protection. You may get an agent to put a comment on the second booking, just for information, but it doesn't help much, there is no formal protection in that situation. You mention that this arrangement is cheaper for you, but it's at the price of losing your formal protection. Informally they may help if there is an irrop, but it's best endeavours only and you may have to pay a change fee. However you look at it, they won't link the booking but they will check your bags through.