I wanted to add that Hoover claimed that Aimee's station, KFSG, wandered off-frequency and that he ordered her radio station to be shut down by the Department of Commerce. There's no record this ever took place.
I'll take you at your word that no record exists. (I don't mean that to come across as unwelcoming as it must sound, of course. You're pretty sure, though, that nothing in the records at the Commerce Department or in Hoover's papers indicates that this agency had dealings with McPherson over this matter?)
At this point, then, I think it might be worthwhile to contact a Hoover scholar or two or someone at the Hoover Library, asking for solid documentation for Hoover's claim. It would be revealing, I think, to see whether you get no further than a reliance on Hoover's reminiscences about dealings with McPherson. A good historian should be willing to consider the issue of lack of primary documentation. (Perhaps you've already gone this route.)
I've had a couple of radio history experts see what I've written so far, and they say that my only problem now in 2010, is how can I stamp out a rumor that is about 85 years old and sounds so good?
You know, it's not impossible to upend a common misperception about a historical event; in fact, it's frequently done. One of my favorite examples is Libby Hill's effort to debunk the popular notion that 90,000 Chicagoans (at the time, 12% of the city population) died as a result of waterborne diseases after a flood in August, 1885. This was a commonly accepted bit of folklore (not only in Chicago, but also in engineering and environmental circles) that persisted until just a few years ago, when Libby started looking for contemporaneous accounts of skyrocketing mortality rates due to cholera and dysentery and whatnot. She discovered that there were none to be found; she also discovered how this bit of "history" came to be.
Your dilemma, as I see it, is that this isn't merely an issue of combing through newspapers of the day for reports of the Commerce Department's communications with McPherson over radio frequency; you have to be certain that no folder on the subject is held in some dusty file cabinet in the Department's basement. Towards this end, then, I think a tactful inquiry with a Hoover scholar or some expert on the history of the Commerce Department might elicit a little extra help with the search for a presumed paper trail.
Good luck, Jim. Let us know what you find out.