Not sure if you've tried this but within the Work Inbox you can view the appointment requests by producer instead of by carrier. Just click the (Group by) Producer button at the top left corner of the Work Inbox screen to see what this looks like.
This essentially does what you're asking but just within the Work Inbox instead of the Info & Appointment screen. It also has the benefit of showing you all of your producers' requests and what stages they are in rather than just a single count regardless of the stage.
Let us know if this doesn't work for you.