Marshall,
Having refinished two bathrooms (
one rear,
one center), I feel qualified to offer some advice here.
It is difficult, but you should be able to unscrew the the drain from the bottom of the sink (it is threaded into the black ABS plastic 1-1/2" pipe). You can use two screwdrivers or even fashion a tool out of pipe (cut out a cross in the end) to do it as well. I do remember being amazed at how tough it was, but it will come out.
If you cut it, you could easily rejoin it with an ABS coupling. (But the drain/strainer will be in your way for refinishing.
As for sink repair, fiberglass/epoxy works well on the back side as long as you scuff up the surface a bit. You can fill in any cracks with resin. Once all repairs are made, you can
apply a couple coats of
2-part epoxy and it's ready to go. Of course, you have to prep it pretty well.