Get the TM30 letter from the hotel with the dates you are staying and take it to immigration.
The yellow shirts can help you fill out the 30 day extension form for about 150 baht including the photocopies. Remember to take a passport photo or that's 50 baht.
It's not high season, won't take long to do the waiting yourself. If you don't want to wait what's the point of your question? Either accept their price or don't
Having a rental contract would confirm to them that you are unlikely a tourist. Never volunteer information like that. I got harassed even I had been out of Thailand for almost 3 months.
Never heard so much nonsense ... even your US Doctor won't diagnose you have a condition and there is no test etc .. and then blames Thai law will risk his life ...