The Miracle has a few problem areas on the top of the radio where the veneer was thin or coming off:

You can see the damage on the left side.  This sort of damage was present on both front edges, plus some misc losses on the back edge.  It would certainly be possible to re-veneer the top of the radio to fix this.  However, it wouldn't be quite right, as the new veneer wouldn't be flush to the front edge, but would actually be above it -- showing a line at the top, when viewed from the front.

Another technique presents itself:  fill the chips with some sort of filler, then paint in the grain.  I haven't used this technique a lot, but it had potential.

Here's the top with the damage filled in with some wood putty:

It doesn't look great...right?  OK, now we need to come up with some paint to fix that.  The key here is to match the color perfectly.  I'll admit, I don't have a great eye for this, but I mixed some high quality artists pigment -- dark sienna and burnt umber.  I then thinned them with mineral spirits and started paint them on:

This is what we end up with.  A little too thick, so I had to thin it down a bit.  Then, spritz a quick coat of lacquer onto it, to seal it in.  Then repeat, until the color is right, or at least close.  You can use some yellow to lighten it up.  I sprayed some black paint through a piece of burlap to add in some grain to the patch.  The entire top was also toned, to give everything an even sheen.  This is what I ended up with:

Not perfect, but not too bad either.  Or, at least not too bad for a first effort at this kind of fix.  You can certainly see it if you know what to look for, or look really close.  It's stil a tad darker than the surrounding area, but it really isn't that  obvious from a distance, nor if you aren't looking for it.

I think this technique has merit, but I'll have to get better at it.