With true married sector logic, it's not always this simple. When you hold LAX-JFK in D class, the system will close out inventory in D class (and often in all fare buckets) when you then bring up availability for JFK-MIA.

Depending on itinerary, could you use codeshares? Where are you travelling from prior to LAX and onwards from MIA? For example, if you were coming into LAX from SYD or HKG with QF/CX, those airlines *might* have a codeshare on LAX-JFK which could be valid even if you have a stop >24hrs in LAX. Or, if you are doing MIA-LHR with BA or MIA-SCL with LA, they'll possibly have their code on JFK-MIA. The married sector logic will typically fall apart when it involves other airlines as AA's system will read it as LAX-QF-JFK-AA-MIA.

Other partnerships like AF/KL have a more robust/sophisticated married sector logic which gives little difference if trying to mix AF/KL codeshares.