This sounds like something that could be handled in the future planned geospacial queries functionality. In XML v2 the SearchBirdseyeInflight endpoint allows for searches by estimated arrival time and destination airport. Does something like the query below match up to what you’re trying to achieve?
https://flightxml.flightaware.com/json/FlightXML2/SearchBirdseyeInFlight?query={< arrivalTimeEstimated 1566921600} {= dest KLAX} {true inAir}
Otherwise it may be useful to keep some general metrics on how far you need to page back in the results for a given airport so that the howMany can be scaled to get a closer approximation of all the desired results in the first web request. It isn’t a perfect solution, but it should reduce the probability of a flight being missed between en route requests by reducing the number of web requests made.