Interesting post, I have the same set (The Anderson aka Mr Anderson) in the same ratty condition and was planning to do basically the same thing, however I was planning on veneering right over the existing whatever it is, I like your method of stripping it down to bare wood better though.
I thought the plastic veneer was Formica or a relative of it, Melamine perhaps?
I don't know if Melamine and Formica are related but they seem similar in some ways.
Would it be easier to just sand it off with some 80 grit or would that take even longer? I certainly wouldn't breath the dust if I tried it.
