Hi, I'm the American wife.
I wanted to give a more detailed explanation of how everything went, in case someone else reading is in the same situation. First of all, I think the idea that it depends on the mood of the immigrations officer is 100% true. As my husband said, the woman who helped me had just started her shift (she had only had one other person before me) and she was in a chipper mood (such a surprise at immigrations!). I started by being cordial and friendly and asked how her day was. We spoke in English, if that is of any significance, because she greeted me with a "hello." I handed her my passport open to the reciprocity reciept sticker. She looked at that, then my main identification page, and then found my most recent entry without having to peruse the entire passport. I think that may have had something to do with my luck as I've had previous officers look through the whole thing and notice that I've overstayed more than once (as was the case, when I left the country 10 days ago, with the woman who told me that four times overstaying were too many and I would not be allowed back in the country...but that woman was, by contrast, in a miserable mood when she attended me).
After seeing on my most recent exit stamp that I had overstayed, the officer asked me how long I would be in the country. I said, "Actually, I'm planning on starting my residency. I'm married to an Argentine." She to pointed to the note of overstay on the stamp and said to be careful with overstaying again and that I had 90 days to get my residency. She took my picture and thumbprint, asked for the address I'd be staying at (I gave our home address), and sent me on my way. It was a major relief.
If there was anything I would have done different, it would have been of course to pay the renewal fee on time. My husband and I actually went to Migraciones in Puerto Madero to do so before my 90 days were up, but the officer there told us, as an overstay wouldn't affect my ability to get my residency that it wouldn't be worth the money to pay that and then the residency fees. He was definitely trying to help, and at the time I figured I'd be here for the rest of the year. Unfortunately, I had to go home for a funeral unexpectedly just a couple weeks later, and well, you all know what happened. Anyway, lesson learned- better to be safe than sorry.