I think the LOD program was fine. Everyone had their turn, everyone knew what they had to do, and 99% of the time the LODs were very responsive. It's better than calling for a leader/manager over and over and no one answering. Sears tried to institute a Manager on Duty program several times in the last few years I was there and they always failed miserably because no one ever wanted to be "in charge", including the store manager.
That being said, it does make sense to call a specific leader if the question pertains to their area. If the Style TL is there, it would only make sense to ask them a Style question. Same with HR, GS, SFS, etc.
As for schedules, we have the Leader schedule for the month posted on the wall in TSC.