Welcome and congratulations on your new baby! There’s quite a bit of information on polishing toons so use the search function at the top. That said, from what I understand, it’s a hell of a job and one that you’ll likely have to do again, but it does look great when it’s all said and done.
Personally, I came from a fiberglass boat that I constantly waxed and it shone like the sun, so it took a paradigm shift to accept the fact that my toons will never look like the day I bought the boat. Difficult at first, but now I’m at peace.
Never had carpet, but I think a power washer might just do the trick. Enjoy…