I cut the box down to be just over 1.5" deep. I was able to get the bottom off finally, but only be destroying the scraps of sides that were still attached. Those nails were really rusted in and were not coming out.
I reinforced the corners before I did much more work so the box had more strength. I've decided to screw 'n' glue the box closed - it works for a guitar so why not a fiddle? The sides are so thin, I am not convinced a glue bond will be secure over time. So I"ve added screwing blocks above and below the soundhole cuts, and plain little black wood screws will go in to hold both the top and bottom.
I was going to bolt the neck on, but in the end it seemed easier to to a dowel all the way through the box. That will give enough strength to stand up to the tension of the strings.
You can see the bits of kerfing along the top edge inside the box - for a bit more adhesion when I glue 'n' screw. I've since put ones along the bottom edge as well where the sides contact the back.
In the photo below you can see the notch cut out at the tail end for the saddle, which will keep the tailpiece cord from digging into the fragile old box. It glues directly onto the maple tailblock.
You can see in this photo that I have flipped the lid - the color on the inside was better but I lost the tax stamp. :-(