The owner (unknowing DIYer) stripped and sanded (prepped) the lower woodwork, for refinishing, then realized the top can't be as easily prepped, is different material, when trying to sand it. I suspect the melamine(?), itself, can't be easily removed, so his alternative may be to stain and/or paint.
Stain won't work, paint could.
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Might there be a relatively easy way to remove this topping, itself, to install a new countertop covering?
Paint thinner will soften/clean up contact cement (the regular type at least, don't know about the waterborn). However, you need to get the thinner between the laminate and the substrate; heating it will soften enough to get a putty knife in at a corner, add thinner, wait a bit, pry some more, add more thinner, etc.
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Can a new wooden top, or veneer, be glued onto the existing dresser top?
Wood, sure but you'd do better to sdrew it on from inside the cabinet. If that is done, there would be laminate edges showing, just add thin trim to cover.
Veneer is possible too IF the laminate is solidly afixed. You would still have the laminate edge showing, same cure as for solid wood except it would be better to apply the trim first, trim flush to laminate top then apply veneer. Here's a reliable source for veneer...
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Some is available in large sheets, no need to glue up individual pieces.
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Might a counter top, as this, able to be stained and/or painted, and get a good adhesion? If so, what might be a procedure (and/or product?) for prep?
Sand, prime, sand, paint
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Best guesses are welcome, since I don't know, exactly, what material this top is.
Looks like plain old laminate. It comes in various thicknesses.
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