In general, when beees draw new comb, it mirrors the comb on the adjacent frame. Is the neighboring comb extra thick? That will make the new comb a little thin. Try to set up your comb in a way that puts new foundation next to nice straight flat comb.
As for supercedure, empty cups are pretty meaningless. Bees will have empty cups scattered throughout the hive pretty much all year. Torn down cells are sometimes harder to spot but would be a much better indicator that a "queen event" has occured. Supercedure or not, I don't that has much to do with the skinny comb issue.
Hope that makes a little sense
