If the information is ultimately disclosed via 404 S-K, does it matter that it wasn't disclosed in the first instance? What consequences could the time disparity have?

Presuming that these transactions are meaningful to the market, a lot. We (like the SEC) presume that people care a lot about disclosed conflicting interest transactions, not necessarily because of the dollar value, but because they may be a sign of deeper agency costs--along the lines of: "They're admitting to taking this much from the company--how much are they really taking? Are they serving the corporation's best interests?" Say that a rational investor would sell on this news. If it's delayed for up to 11 months, and then "buried" in a proxy statement loaded with a bunch of other information, then the conflicts-minded investor has to wait to learn the relevant information (and sift through a bunch of other stuff). During the delay, the stock price could well tank, as the officers continue to make self-interested decisions and the company suffers.

Looks to be a great project! I haven’t read the paper yet, but I think it may be a mistake to dismiss Lori's observation on the basis that the disclosures you are studying may well prove to be material.

There are many circumstances when disclosure rules require the disclosure of information that is not material, even indirectly. First, and most obviously, mandatory disclosure generally rules do a poor job of requiring the disclosure of the various types of information that sophisticated investors actually use to value firms (that’s what I’ve found, at least). It seems quite likely that a disclosure rule involving waivers of codes of ethics simply misses the mark, if the intent were to improve share price accuracy. Second, even well constructed disclosure rules may require the disclosure of information that is not material. For example, as you point out, Mahoney argues that the sole benefit of many disclosure rules is to reduce agency costs (elsewhere I’ve argued that Mahoney’s claim probably overreaches, but his point is probably valid at least some of the time). There is no logical reason to assume that reductions in agency costs are material. Finally, requiring disclosure can help to reduce fraud, again a benefit that may be independent of the materiality.

The better response to concerns that information regarding codes of ethics is not material might be to agree that this particular disclosure provision may not be representative of more obviously material information, but at least it provides a starting point.