Yes you are right gel coat is different to a extent then your base coat or base coat clear coat.
Gel coat is pigmented polyester resin which gels against the mold surface.
But if you look at what is in clear coat you will have poly,urethane,acrylic.....a type of resin.
When I buff a car or boat I take the same steps. #1 check for scrathes in the paint or gel coat(if it's a car clay bar it first). If I have to I will wetsand and compound .#2 Once the scrathes are compounded out I will pressure wash(pressure washing removes the grit) then use a cleaner/wax this will remove any of the compound scrathes. In steps one and two I use a makita buffer and a Porter cable orbital for step three .#3 I use a orbital buffer to keep from having any swirl marks in the paint or gel coat.
What I was trying to show with the pictures was that for the most of it,it does not matter how bad the paint or gel coat is it should buff out if you take it to the right Detailer
I have never come across a boat or car that had shoe polish on it .You want something that will dissolve the shoe polish but not hurt the paint. I would try baby oil or WD-40. First put the car in a shaded area make sure that the surface is not hot. Then I want you to find a spot on the car and test the baby oil and WD-40(One drop from each sray WD-40 into lid and dab it on car don't spray directly onto car it will make a mess )Make sure that the test spot isn't noticeable. Leave on car for about 15 min then wipe off. If it did not hurt the paint then go ahead and test on shoe polish. Do only one spot first and if it worked then proceed onto others.Afer your done wash and then wax the car to make sure the oil is off the car.
GOOD LUCK AND THEY ME HOW IT WENT!!!!