I am not sure what you mean by "Overturned", if the diagnosed was right and you were on medication then I doubt any doctor will certify that it was a wrong diagnosis and they put you on meds just for the sake of it. I recently did my medical and I got my SI medical certificate / ticket with a condition, without going into too much details all I can say is when I showed up at my AME's office and handed over my history to him he said yeah you had a disqualifying condition, but its under control now and you are not on any meds that is prohibited by FAA (I was 2 years back), they wont care. He gave me my ticket on the same day, normally as far as I know, for SI, everything needs to be sent to FAA and they issue the SI and the AME can sign off on it from the next year. for me, since my condition was under control, FAA didn't even blink.
Note: your situation may be different. I will let any AME or sr. members to comment. I have read elsewhere/ other threads that it might be a good idea to find an AME who is a pilot / retired pilot, set up an appointment with him for consult , DO NOT fill up the MedxPress form and submit it - that becomes official. if the AME says, no you cant get a SI, go for Sports Ticket. or wait and see how the Private Pilot Medical reform plays out later next Aug / Sep in real world and take a call
