Will US TECO office approve 60 visa after recent ARC expiry?

I’ve read through pages of posts and utilized the search engine, but I was unable to find any thread that addressed my specific situation, so my immense apologies if this is a terribly redundant question.

I finished my old job (and ARC) about two weeks ago, and I am spending the summer at home (USA) until early August, when I plan to return to Taiwan. I already have signed a contract with a reputable school for a position that will begin on September 3rd. I was told by my school that I should apply for a 60-day visitor’s visa, since I was hired by this school two weeks before I left Taiwan, and did not have anytime to extend my arc (not to mention it would be impractical, considering my position doesn’t begin until the fall and I really should have a one-year ARC from August or September).

I have already purchased my flights for a “two” month stay and I will be applying for the visitor’s visa. My question is this: What are my chances, realistically, of getting a visitor’s visa through a US TECO office, when they can clearly see in my passport that my old ARC just expired and that I had a previous visitor’s visa? I am applying through Chicago, which has always been friendly and helpful, but I’m nervous about this specific situation.

If rejected, I know I can go on a visa run once I am in Taiwan on a landing visa. But I was wondering if there will be a problem with the airline if I don’t have a two month visa when I initially arrive, since I have a flight for a two month visit. Would I be unable to enter Taiwan on that ticket?

I’m obviously ignorant about all this, so if anyone could either answer some/any of my questions or point me in the direction of helpful threads, I would be very grateful. Thanks!

Call them and ask them. And get a name when you do for future contact regarding what they tell you.