This thread has gone on long enough that it piqued my curiosity, so I consulted my dictionary. My dictionary says "yesterday" can be an adverb or a noun. As an adverb, it would be incorrect in the "on yesterday" phrase. As a noun, it would not be. Unless I'm missing something, based on my two-minute research and pondering, "on yesterday" is not an incorrect usage, even if it does sound odd.

If it's up for a vote, I vote for absolute dates rather than relative dates. If relative dates are appropriate, I think "a week ago last Tuesday" and similar formations should be considered.