I'd assume that it's a latex stain on there(Magnepan would know)and the clear coat.
Actually menthyl hydrate takes off latex paint,which you could try to see if any comes off,if it does not,then you know for sure it's oil base.we use it all the time to see if paint is oil or latex.
A few swipes with that on a rag will let you know right away.
If oil it just stays shiny and nothing comes off.
Also perhaps a natural paint/stain remover would take the bulk off.
Then fine grit sandpapr to get in the grain,perhaps starting with 120 grit and going to 180 up to 320.
A petroleum based remover is nasty too work with.
Before all that make sure you MASK the whole panel off as no matter how careful you are it seems to places where you do not want it to go on.
A cabinet making company can help also.