@Christine ****
a Special Tourist Visa cannot be changed to any visa inside the country
Whether you can or can't get the conversion done on a 30 day visa exempt entry depends entirely on you and how fast you get your ducks in a row so you can apply for the 90 day Non-O visa at the immigration office where you live.
Most offices require a minimum of 15 days left on your current stamp to apply (SOME Chiang Mai and Phuket require a minimum of 21 days).
So what that means is; if you think you can come in on a 30 day visa exempt, get your sh*t together document wise fast enough and go apply, do it.