I am also tempted to say Kalanchoe. I am not familiar with that genus, though, so I won't be much help there. What you can do, however, is to improve the soil and light. For soil, you could mix together 60% perlite, and 40% cactus and succulent soil.

Roughly what location are you in? Right now, I would give your plant as much light as possible (sunniest window, etc.)

I am in Zone 5B. I have a relatively sunny southeastern-facing window. So, I've moved the poor thing in there next to the echeveria I bought at the same time. I was just going to run over to Home Depot to get some cactus/succulent mix. Thanks!

I would still love to hear if anyone has a different guess on the ID of this plant.

Yes. Give it the sunniest window possible. You could also look into grow lights. If you live in a area with long dark winters, grow lights are pretty essential.

I have a grow light I'll add that, too. :-)