There are concrete repair products made for recoating, they possibly
have Vinyl in them or some other plastic and are designed for thin
resurfacing. I dought it would last for more than 5 years but for one
step it would be worth trying, There is a machine made by Porter Cable
you might be able to rent it is a diamond rotary tool that gouges in
groves like the ones done on road resurfacing, but handheld and 1000$,
If you cant find a rental, Bleach should be used to kill the mold,
Muriatic acid to etch it and power wash ot just wash it good. Or cut a
drain grove in the concrete with a a power tool, grinder or circular saw
and conctete blade.