...I just received two phishing spams from the same spammer yesterday. However, I couldn't report either one because the date in the header reads May 22, 2008. This is obviously a ploy to avoid being reported.
Is there still a way to report this clever spammer's phishing attempt?

No (you mustn't alter anything in the spam to make the parser accept it). But without a
(link) it is impossible to know what the actual problem is - it is not likely it is a spammer ploy. See the discussion at