It would appear that someone had a few tee many martoonis, and decided to paint the blistering and finish-eroded veneer on this job.

Gad I hate it when people do this...
If this radio were mine it would prove tempting to say "let's not lie about this radio's own history, and simply fill in and smooth out the missing veneer and leave it black.
Such procedure--while perhaps heretic in nature in some antique radio people's philosophy--would certainly be cheaper of time and money than the stripping-down of all that junky paint, and inlaying or entirely re-veneering all that cabinetry.
Whatever you decide to do....good luck in the project, and I hope all goes well.