try this
Drill holes in the furniture in the front, then use canned foam and CAREFULLY squirt insulation in. Do this a little bit at a time; you can break things with this foam.When you are done, plug the holes with teak plugs, sand smooth, and varnish. If done properly, they will not be visible.This is not ideal, but it worked fairly well for me. A better solution is to remove the counter top and place vacuum panels around the outside of the box - however, this is a lot of work, and I still cannot figure out how to get the top off without ripping up a lot of stuff in the process.You could also insulate on the inside of the boxes, but you will lose space and it is not clear what type of material to use or how to secure it.good luck!MC