Usually, luck control is already there in skill tiles. If you also get to choose cards, it might too much.
That's a good point - I have not played the game enough to know if this a "tipping" issue.
I think might then try my original idea, which is allow you to draw (unseen) from the draw deck in place of any draw from the face-up set. This is a similar mechanic to "Ticket to Ride" and "China" and at least allows for some element of choice. ("Will Fate guide my Destiny" and all that )