I just went and looked at the one in my kitchen, it is not fastened on the bottom like yours. it is fastened to the cabinet above it, and it slides up inside the trim of the cabinet above. If yours slides under the cabinet above and the edges do not show, that would be the best place to trim and it would not show... I know you said you can't take it out, but if you could that is the way I would do it. If you can't take it out but could get one of those saws you mentioned inside the top that may work. I'm just saying if you cut the top the cut part would not show if it slides up into the cabinet above... hope this help maybe just a little.