So very confused (multiple visa questions)

Alright, so I posted a similar thread about this in the “Living in Taiwan” forum, but after further investigation concerning a visa, I’m even more confused.

Quick background: I’ve studied in Taiwan three times already, really liked the country, and really want to go back.
I’m graduating in two weeks, and hope to work in Taiwan.
Ideally, I’d like a non-English teaching job, but from what I understand, you need two years work experience to get a work visa for anything else.
I (most likely) have a job offer for a proof-reading job, but I confirmed with someone at the company that they cannot get a work visa for me, because I need two years experience.
I confirmed the necessity of this in the other thread, and from what I gather there seems to be no way around it.
Today, I went to the TECO in DC, and was hoping to clear some of my questions up.

If I understood her correctly, I CANNOT go to Taiwan on a visitor’s visa and switch to a work visa (other threads in this forum seem to confirm that…others don’t). In order to apply for a “work” visa here, all I need is confirmation of a job offer in Taiwan. She said that the TECO office doesn’t deal with the work experience requirement, and that’s the job of the people in Taiwan…I have no idea what that means.

I can’t afford a round-trip ticket (hurray for being a student!), so I’m counting on getting a job before I leave, but I’m not sure exactly what counts as a “job offer.” So…if anyone could help me out with this I’d be very grateful. I am applying to a few different English schools in hopes of getting an offer from them, but I’m just so confused about what one needs to do for a visa that I was hoping for some guidance before I move any further.