I've just realized that the walnut veneer I have for patches seems to have not nerly as tight a grain as that on most of the old radios. Perhaps those trees were older and grew slower. Do you have any ideas of where to get veneer which is best for patching?

It's called Australian walnut,check these,http://www.veneersupplies.com/brands/Walnut__%28Australian%29.html !

It's good to have some old salvaged veneer on hand, for this sort of job. "Walnut" can mean a lot of things (though it's not as bad as mahogany, which can be anything that came from a tree). Also handy are the veneer sample kits sold by Constantine.