You'll resolve A Piece of the Action clause by clause, and React as appropriate.
This means you'll-
Play a dude from your hand, reducing their cost by 4, to a minimum of 4; the cost cannot be reduced further.
You'll then check for Grimoires & More, as you've hit it's React trigger.
The dude isn't a Huckster, so you can't React, so you move on to the next clause.
You may search your discard pile for a non-Gadget goods and attach it to that dude, reducing its cost by the amount this card reduced the dude's cost.