Aha!

The reason that our carpet estimate seemed much higher than it should have was due to what I choose to politely call "hidden fees". Some of these were warranted (you pay extra for stairs, for an entry that's not a straight-shot into the room that's to be carpeted, etc.), others were not. (We do not, for example, have any radiators in our basement. Hell, there aren't even any heat registers in the floors.) So we got rid of the ones that were inappropriate, knocked of 10% because there's a sale on right now, and ordered the new carpet. And my head spun with the pain of it all. Thankfully I was vigilant about what each line on the estimate meant.

In 1.5 - 2 weeks, we will have new carpet in our basement. Hooray!