Renew your passport when you get back to the US then apply for the DTV. Applying while traveling adds a bit of complexity (sending photos of passport pages and proof of hotel reservations). Applying while in the US simplifies that part.

Also, whichever MT school you get the DTV through is the one you have to stick with and you better go. I think the school is required to report it if you dont show which will probably lead to the cancelation of your visa.

Finally, the course you mentioned does seem exce$$ive. Not certain where you are trying to live, but it might be worth it to live someplace like Bangkok for a bit so you have more options that might be more budget friendly.