It would pee me off to tiggerific but I think the only way that you can get away from that situation is to adopt a different rostering practice. I guess there would be some form of trade off (eg) it could be done but only by reducing the number of days off you'd get. Starting on a late and finishing on an early would automatically require more workdays out of the employees to make it work.
I'm sure you should be protected from late finshes/early starts before and after requested leave? Ask your line manager about it.