My 2¢ (alt-0162 if you want to do it yourself) worth:
1. On a show where merchandise is not announced as part of the total, it is logical to look only at cash winnings. (The first college champ to win a car was introduced in the following ToC with only the cash winnings, not "$xx,xxx in cash and prizes.")
2. On Super Jeopardy!, contestants' winnings included regular games and ToC appearances. In the Million Dollar Masters, and even in the last ToC, IIRC, no figures were announced at all.
3. I am assuming that the ToC, which has been taped, will air out of order relative to the regular games. If I were the producer, and Ken was still the defending champion when the ToC taped, I would not want him to appear because of continuity issues: Either Alex would appear not to know whether he had lost at the time of the ToC, or he would appear not to know whether Ken won when the games resumed.
4. Once Ken's regular appearances and his ToC appearance have concluded, his total would naturally include both.
5. The reason The $100,000 Pyramid didn't have too big a problem with a defending champion appearing in a tournament is that they had a five-day limit.