What are my options for extending my stay in Thailand with a non-immigrant ED visa?

Okay, I have never seen people who come here on Non-ED visas for internship EVER get an extension inside the country and I know probably 20-30 people who tried and were denied at the immigration office. Even people from real universities who had internship as part of their education couldn't do it.

I doubt you'd even be able to get documentation that would let you get a new 90 day ED visa from any of the thai consulates in the area based on interning but you can ask where you're interning and check the website of the thai consulate you're thinking of using to see

Personally I'd Just go to a thai consulate in another country and get a single entry tourist visa, come in get the 60 day stamp and take the 30 day extension, <- that's the 3 more months you're looking for.

Strange that you're enrolled in a 6 months internship and the school can only provide a 3 month stay, what is the reason why you can not extend?

Alternative is go to a neighbor country and apply for a Single Entry Tourist Visa which gives you 60 days on entry and can be extended once on basis of tourism with another 30 days