Cannot convert 60 day exempt, you gotta enter using the 90 day nu on O and then extend that for 1 year. Total 15 months. Why did you enter on a 60 day exempt when you already had a 90 non O ??
You can do that from inside Thailand too, but it costs a bit more. The really easy way is to get the 90 day from your home country before arrival and then convert to 1 year, for a total of 15 months. Add multiple entry at additional cost.