Even setting aside that ambassador is a factor at some point (I would think at the start, but I can see why some would think later on), you approach this game very similarly to Hunting Party + X... except you have no X. That's a trouble considering you do not easily hit $8... You hit $7 quite often.
Unfortunately, the best "X" is festival, so I doubt festival + multiple HPs would win the game, even unless the opponent is loading up on nobles.
To answer your question, I would have purchased a festival at Turn 10, 12, 13 and maaaaybe 14. Then just gain all the pieces you need over and over with the economy/+buy.