Both versions are perfectly fine. It's really just a matter of stylistic choice (or your choice of narrative reference/relevance time, if you want to get technical).
Arguably repeating would have could be seen as slightly more precise, since it matches the tense of the "primary" verb (I would have thought). That would thus have the possibility of coming across as more "condescending/haughty", which might well be appropriate.
On the other hand, the "present hypothetical/conditional" (you...would know...that) might be seen as even more condescending, since it tends emphasise that you still don't know it.
But these are fine nuances. Native speakers wouldn't normally stop to think which precise meaning they wanted, and choose the verb form accordingly. People use both forms interchangeably.