Is there truly no way to get information about medical application status?
Dealing with the FAA medical is always a tiring process. Best places to consult would be services like AOPA medical assistance, or through Aviation Medical Advisory Service (AMAS).

There are other options probably, but I know AMAS is the go to consulting group for controllers and a lot of airline pilots. AMAS will often help guide you with knowing ahead of time what information you need and what forms to have filled out to try and make the process go quickly.