The guitar sounds about the same with and without headphones. So I think the problem is with the mic in the laptop itself.

I did get a USB Micropphone that I'm plugging right into my laptop (no interface). I was a little worried at first because I was getting a good sound when I spoke (very good, actually!) but the guitar was sounding very low and light. Then I realized that while I had my other sound inputs deselected, I had to actually disable each one. Then I started to get much better sound. I even tested out some things in Audacity and it finally sounds good in there, too. I'm optimistic that this will work really well for what I intend to use it for. My USB Microphone is the Neewer model, the last one that the article Christopher referenced above recommended for this kind of price point (under $50). Overall, very pleased with it!

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