Complicated ARC question

I posted this in the “expired ARC” thread, but it’s pretty different from the question in the original post and I’m really hoping someone can offer some insight.
Here’s the story:
My ARC expires today (so I guess in about an hour). I just re-entered Taiwan about 3 hours ago. In my passport I have a multiple entry visitor visa which has not expired, and I don’t have any other visas in my passport (ie. no residence visa). On the little immigration form I wrote the type and number for my visitor visa, intending to either enter on that or do visa-exempt entry so that I wouldn’t be overstaying between now and applying for my new ARC. The immigration woman looked at the computer and asked to me see my ARC, then wrote down the ARC info on the form and stamped everything. I asked which visa I’d entered on, and she said the ARC, because it was still good. I expressed concern about overstaying, since my ARC would not be good in 4 hours. She basically said that the expiration date just meant that I had to enter by that date, and that I would not be overstaying. I asked a few times in different ways and she said the same thing. Her English was good, so it wasn’t a communication thing, she must have believed what she was saying. I am somewhat skeptical though. It was my understanding that when your ARC expires you have to leave.
So, am I in trouble? If I am in trouble, would I be likely to be able to argue my way out of it, since I tried to do the right thing and have proof (ie. what I wrote on my little form)?
I am planning to apply for my new ARC on Monday, I suppose that if I am in trouble, they’ll tell me then?
And on a related note, what happens if you have to leave the country between the time you apply for your ARC and the time that it’s ready? I have a trip to China on the 10th (for a conference, can’t be changed) and am worried that I may not have my new ARC in time. On various websites I’ve the processing time described as anywhere from 5 to 10 working days. Can you pay extra to have it done faster?
I suppose there’s nothing I can do until Monday, but it would be nice to know what I’m in for.
Between ARCs and all my Chinese visa drama, this month is turning into one giant visa clusterfuck…