Crowded skies and exhausted pilots are a bad mix, the airline industry and pilot unions agree, but they’re struggling over what to do about it. The airlines want to schedule some pilots with less-taxing flights — fewer takeoffs and landings — but for longer, not shorter, hours in the cockpit. The unions say they won’t agree to more hours for those pilots in exchange for fewer hours for pilots who fly as many as a half dozen short flights a day or take off at odd times. That was the main sticking point in an otherwise harmonious effort over the past month and a half to rewrite flying-time rules that in many cases are a half-century old and predate recent scientific findings concerning fatigue. The advisory committee on pilot fatigue was expected to deliver its recommendations to the Federal Aviation Administration late Tuesday. Committee members said the FAA had asked them not to make their recommendations public.