Frankly, I can kind of see their point. You have a ticket to Thailand with a return 45 days later. How do they know you're going to leave the country within the first 30 days? (Or, more on point, how do they know that the immigration officer that you speak with when you arrive in Thailand is going to believe that you'll leave the country within 30 days? If he sends you back, it's on their head. Thus the reason they're concerned...)
At this point it seems you're in a bit of a pickle. My oversimplified advice to you is: what's more difficult at this point, fighting Delta or getting the visa?
Thailand has an embassy in DC and consulates in LA, Chicago, and New York. Their website indicates you could get the visa within 2 days if applying in person and it costs $35. Hopefully someone with more experience can chime in and offer better details.