IMO get rid of the carpet. It will always hold dirt, moisture, odors and worse.
a)fashion a new sole from whatever material may work, teak is traditional but expensive, other options may be available, especially nowadays with all the synthetics available. At $250 a 1/4"sheet, the traditional "teak & holly" plywood will make for a costly project - looks great though and depending on boat size you may not need too much of it.
or b) fair the fiberglass sole and paint it with a mild non skid, perhaps in a slightly contrasting pattern to get away from the mass of white.