After doing one of these with no prep, I found that splitting the difference worked.
I would lay out a random spread a couple days before they got to that part and write down an interpretation of the cards at my leisure. Any card can be shoehorned into pointing out things you want it to if you have enough time to think of the right words.
Then I would shuffle the stat cards, let them draw, then pretend to shuffle those back in and lay out the spread according to my already written interpretation.
So it was still random, just not so random that I actually had to think of prognostications on my feet. Also I didn't feel guilty for purposefully putting too many (or too few) of the stat card in the spread (since it was a random draw).