Re: TSP or Car Wash soap?
If the hull is chaulky, then it's most likely that you need to buff out the gelcoat. TSP will certainly go a long way toward removing yellowing and won't hurt the gelcoat. It may eat away wax but in your case, it doesn't matter.
There are a few threads in the resto section about restoring jelcoat and people have different ideas and experiences. For my old boat, I had to keep using more agressive cutting compounds until I was able to get down far enough to remove the chalkiness. Only after buffing out the gelcoat properly, was I able to get the shine to last.
Good luck and remember that Advil is your friend on this one!