I could tell by the brown crystals I could see in the wood grain that the original veneer had been put on with hide glue - the real stuff cooks out of animal tendons and hooves and such. It is still used today particularly on things like musical instruments. The reason for this is that it has the excellent property of holding things like iron while dry and letting go when it is heated with steam. That way a guitar or violin that has been assembled with it can be disassembled for repair without damaging the wood. I wrote a small book on this a while back. (Heath, Maya, A Practical Guide to Medieval Adhesives, Issue 134 of The Compleat Anachronist, Society for Creative Anachronism, 2007.) I did a lot of research and experimentation with various kinds of pre-industrial glue for this. What made me cautious was the delicate under surface of the carcasse wood and the less than robust condition of the box as a whole. I didn't want to have to do a lot of digging and prying to get it to let go. All the blogs and videos on the internet I could find deal with flat surfaces. Getting steam and heat to this compound curve were going to be a challenge.
I took an old wash rag and got it wet just a little drier than dripping, folded is in thirds and laid it on the veneer I wanted to remove. I took an iron and heated it up to maximum, then laid it on the wash rag.
I didn't leave it on there long - maybe 10 seconds while I picked up the camera and took a couple of pictures. There wasn't much danger of the rag burning as it was hissing and chortling steam like crazy. Then I lifted it off.
Using an old cake spatula I began to try lifting the edges - GENTLY. You don't want to be digging at the wood, just letting the heat and steam do its work. The edges began to lift up. I had to apply the rag and iron a couple of more times before it lifted away altogether. The key here is that you have to work with the glue and veneer are still really warm to the touch. Once it cools, its set again.
It took a bit of patience working one area at a time. It didn't always come off in convenience large pieces, but eventually it did all come off.
Now it needs to sit a while drying out. I didn't get it damp to the touch, but all that steam forces itself into the wood grain. So it needs a few days peace and quiet before I hand it over to Phillip to glue back together.