Hmm. Back in the mid-late 1980s, I believe that H&K made a sick looking variant on the HK-91 or G-3 type rifles that had Wooden stocks, like a classic Sporting rifle. After the GWB ban went into effect, they went bye-bye, at least for US imports.
(I know it sounds crazy, but I swear I saw it in a catalog. In 1980s dollars they cost a ton, too.)
What's to stop someone from, instead of making a stock like the one in the story, mating an AR to a Sporting style stock? There is the buffer tube, which is the big issue, but one could slip the stock over, whether a wooden one or a molded plastic one with a wood grain look to it. A matching fore-stock should be doable with either, too. The pistol grip thing is interesting. In the picture shown it looks like an FJ-42's, but could it be eliminated entirely? In the Klintoon Ban days they used thumbhole stocks.
Throw on a classic set of mounts for a scope, which should be doable with a top rail, and a classic hooded front sight perched on the usual post. Rear iron sights can be done several ways.
An AR-15 or AR-10 type rifle kitted out like this would be pretty neat, actually.