To clean gel coat I use 3 different common chemicals, generic CLR which is an acid that is great at removing mineral stains. Simple green which removes greasy oily stains. Bleach which is good at removing stuff that was living like algae and scum. In your case I would try liquid bar keeps friend which is oxalic acid and mild abrasive. Just use all the common cautions as it's very strong and needs rinsing before drying. If that doesn't work maybe comet with bleach might be my second try.
When non skid is clean and dry you can actually wax it with the wax in an orange bottle called NU Finish at Walmart. It does not make it slippery, but test a section first to make sure you trust it