Very cool - and cool that you would remember.
I picked up a little WFAA related souvenir from 1933 a few years back on ebay. It is a "radio log" book distributed by The Dallas Morning News
and WFAA for ten cents. Most of the log book is copyrighted by Haynes Radio Log out of Chicago. Apparently Haynes published customized versions of the log for various newspapers and radio stations across the country.
Since this board does not permit images to be included in postings, I have uploaded images of the WFAA specific pages of the log book for people to view at: http://www.radiodismuke.com/wfaa/
Observe that there is ZERO mention of WBAP with which WFAA shared the 800 frequency. And this was still a few years prior to WFAA and WBAP alternating between 800/820 and 570. I especially like the image of the Grapevine transmitter building that was torn down years later when they built D/FW airport. As for the image of The Early Birds of WFAA - sure would be interesting if there were surviving transcriptions or air checks of that program. My guess is it is unlikely.
The non-WFAA portions of the book provide a listing of every radio station in the United States, Mexico and Cuba. There is also a listing of all the major short wave stations which could be picked up in North America as well as the frequencies on which police calls could be heard in various cities. The book also has a section where the radio dial is broken down by frequency with columns listing all of the stations on those frequencies by region. It also lists each station alphabetically with information about signal strength and any national network affiliation.
There is also a chart broken down by day of week and evening hours between 6 and 11 PM on which listeners could log the stations they were able to pick up.