Wet sanding is the only sure way of bringing a lasting shine back to dulled gel-coat. Over in the Whaler world we have been doing this practice for years and I have done it with all of mine. While it is more labor I usually start at 800 then go to 1200 if I do not want to do a heavy wheeling of compound.
In the spring I am planning on doing this process to my new to me 190 Tournament when I remove the old stripping.
As for removing bottom paint, many in the Whaler world have been using the process of soda blasting off old bottom paint down to gelcoat. Some like myself have chemically stripped the old paint off too. That is a pain though. From the raw stripped finish they start with a quick 200, then 600, then 800 and finishing with 1000+ grit. By the final sanding any remnants of the old paint are long gone and after a good buff / wax you have a nice clean bottom.
The other option if you keep your boat in the water but do not like the look of bottom paint is tohead the route of using a custom tan bottom paint. I had some mixed up at a local marine paint manufacture here in the Detroit area to match the gelcoat color of my old Whaler. I really liked this option.
Here are some
images of the process....Here is a side by side:
Before:
After (yes there is bottom paint on there):
PS...The tournament I bought in Jan is my first step into the Grady world. The last 20+ years and 8 boats have been filled with owning and restoring Whalers....so that is where all of my background is. But all the techniques relate and translate....