I think the problems mentioned can be easily avoided by adding only certain cards to the Secret pile, e.g. only $5 cost cards, or cards costing at least $5. Or the same for $4 cost cards and Secret Breakthrough costs less. One could also include a gambling factor, e.g. 1/3 $3, 1/3 $4, 1/3 $5 cost cards with Secret Breakthrough at $4.
I've done similar cards (not Events), but with custom cards in the pile. The fun starts when you add some real surprise cards to the pile, like hot potatoes changing owners after play and giving -VP or +VP; or Pasture-type cards that can influence strategies a bit. It's fun, at least for players who don't take the game too serious.
Edit: I think you don't need "You need not show...".