I did talk with my roommate about the table, explaining that the water/heat from the dishes caused the finish to separate from the wood, forming the white rings, and what she thought was spilled food she was scraping off was really the finish. She said "well we've got some stuff in the lab I could try to put on it to fix it", an offer that was quickly but politely declined. (You've done enough, stop while you're only a little behind!) I explained that with the sentimental value of the table I didn't want to be monkeying around with different things, so I'd see how much it would be to get someone to refinish the top and go from there.
She did offer to pay, and it was an honest mistake on her part. She even moved the table out of the way and has been using an old TV stand to hold her meals while she eats in front of the TV. I feel bad that I didn't catch it earlier and warn her before the damage was done, so I won't make her pay the full cost. Over the weekend here I'll scout out prices of the different options.
Lesson learned on my part - if I even have the slightest doubts about anything in the future - address them. Be Miss Obvious so this kind of situation doesn't happen again. I can't remember whose sig it is that says "Never attribute to malice that which can be explained by stupidity", but it's so true!