Below is what I'm looking at. It's two versions of the same layer. The first, in green, is straight from ArcOnline--it's not stored locally, and has not been reprojected, so I assume that means it is just being projected on the fly to match the data frame (where I've set the Backwards Krovak). The second one, just the outlines, is the exact same layer, I just exported the data using the data frame's coordinate system (so again, the Backwards Krovak) and now it is of course stored locally.
Features are labeled as you'd expect, just using the State_Name field. No other label expressions going on. I tried something similar with a world countries shapefile, and once again, only a select handful of labels were shown, and they were all over the place in the wrong location.
Since I feel like I'm playing with cartographic fire here, I really wouldn't expect the labeling to go smoothly, but I am curious why it shows as it does. It would be neat if I could get it to work.
If you have any thoughts, or can pass this inquiry along to the labels team, that would be awesome! Thanks for your initial reply!
Follow up question, if you'll have it: If I wanted to display some other county backwards, would I just play with the LAT and LONG center parameters to center over wherever I'm interested in? Or are things more complex, and I'd need to somehow figure out what the azimuth and rotation would be changed to as well?