Rotating counters & layers

I’m working on a change to a module and I want to show counters with both facing (permanently on the counter, part of the image) and direction (switchable on and off via a layer on the counter, hopefully changeable with rotation). For this to work, I will need to be able to rotate the counter (to show facing changes) and the layer (to show direction changes) separately. By fiddling with the order of characteristics, I can change the facing without changing direction; but rotating the layer to change direction also changes the facing on the counter. Is there a way to be able to rotate the counter, and the layer, independently? Any ideas appreciated; thanks!