Hey Ryan,
Interesting question! There is not a way to do this right out of the box, I’m afraid. I believe it would require touching the core files where the post types are registered in order to do that, which I wouldn’t recommend doing–mostly because those changes will get lost in future updates.
That’s a cool idea though. Would you mind adding it to our feature request forum? It would be interesting to see how many other people would like it as well.
Sorry I don’t have a concrete answer, but does this help answer your question? Please let me know.
Cheers!
Geoff