I just bought one from an antique mall that needs a dial scale cover and new pushbuttons.
Having done some research on the web, it appears as if the pushbuttons from RadioDaze may be too short for the '39 models, and the supplier for the 'long' ones (www.antiqueradioknobs.com)
seems to be defunct.

Do any of you have any experience with this, or am I going to have to get REALLY creative and try to manufacture my own substitute knobs (or modify the ones from RadioDaze)?

Renovated Radios has long push buttons for 1939 sets:
http://www.renovatedradios.com/parts.html

Thank you, Carl: that site is now on my favorites list!