You also seem to think 30k is the 100% bill rate. A successful consultancy looks to be closer to 70% (and successful in this case means that they don't actively seek customers). The other 30% doesn't come from vacation, it comes from overhead.
The Bingo Card Creator falls into the same spectrum of charge out as Patrick's posted consulting engagements. Whether it was more or less is largely immaterial because consulting engagements are things he's been actively avoiding for a long time, while being done with Bingo Card Creator is something he's actively engaged in.
I'm not 100% sure I agree with Stavros' point, and I'd guess that there was a lot of downtime in the 3-week sale in which Patrick was doing other things, but if you read the situation as Stavros proposed it, the economics are the same -- as $63,000 > $57,000, it cost more to sell BCC than to keep it.