If it is a fishing boat, bite the bullet and drill. But no to fast! First find out if the cabin surface you are going to drill is core construction. Most fiberglass boats cuddy cabins are corded.
If I confused you let me explain cord. Core is a layer of glass with a balsa wood type fill and then an outerlayer of glass.
This type of contruction is usually about 3/4 of " thick.
When yoo drill use a bite one size smaller that the screw size. Tape the drill so that you do no go through the outer glass skin.
If the cabin is solid glass, chances are it will not be thick enough to support drilling.
You could cut the carpet round the frame of the rod racks and peel the carpet. Next clean the exposed fiberglass with sand paper and solvent to remove all dirt and glues. Next apply a good sealer like 5200 to the back of the rod rack and press into place. clamp of shim the rack for 48 hours allowing the sealer to full cure. Also make sure that the surfaces are over 65 degrees. Once done the racks will be part of your boat forever.