Filling gap beneath hardwood floor (between floorboard and foundation)
That's a good solution if you can hammer the wood piece in tight enough and below the bottom of the flooring.
Also you could pour in a floor leveler to the same height as the existing floor. Once it's cured cut a strip of flooring so that there is a 3/8 inch gap between the piece and the fireplace apron. Glue it down with a construction adhesive.
You could also remove the trim pieces that frame the apron. Install wider trim pieces to cover the gap (leaving room for expansion). Apply colored caulking to fill expansion gap.