Nicole, you've done nothing morally wrong and have nothing to feel guilty about. You made an error, admitted your error and done more than is really necessary to correct your error.
As an example: while traveling, you accidentally shortchange a 7-11 clerk a dollar, complete your journey of 300 miles, and make the discovery of your error. Would you make any effort to correct the error? I don't think any rational person would expect you to go to any effort whatsoever, not even the 7-11 clerk or owners of the store. The action was unintended and the amount inconsequential.
This copyright issue is the same. Your action was without harmful intent and financially inconsequential. If the NYT were to pursue legal action, it would be irrational. If they were to pursue any kind of financial remuneration from you, they would be trying to take undue advantage of you, and you should neither agree nor offer to do so.
I believe that most likely you will never hear from the NYT. If anything, it is more likely that SOLO would be contacted, informed of the infringement and instructed to remove the article. But I doubt even that will happen.
Like all federal law, intellectual property law is convoluted and byzantine and the rules for the internet are still being written. I've had enough experience with both copyright law and large corporations to know that the best thing you can do now, regarding this issue, is absolutely nothing.
As I said previously, Nicole, you rock! Good luck with your exams and forthcoming nuptials with whomever the lucky guy is. :-)