Seems like a lot of people would write "The car which I wound up buying was a Honda."
Yes, and a lot of people spell "you're" without the apostrophe and the e. This isn't quite incorrect, I guess, but it just sounds awkward. If I were editing their copy, I'd change it. In fact, this is one of those situations where it doesn't need either a "which" OR a "that," so I'd just delete the whole word.
I looked back over the two previous sample uses, and my car example didn't need a "that," either. But the "baseball" example does. So maybe "that" is a definition when placed between a noun and the verb that follows it?