I too first thought you were referring to the Air-Mail Saves Time slogans.
Somehow you have found a reference which is incorrect or you may be misinterpreting it.
Regular stamps are valid to pay airmail postage, special delivery fees (by this time), etc. Thus there is no such thing as overprinting regular postage stamps to change their category. Or anything related to shortage, etc.
Here is an example of a pair of Northwest Territory stamps paying the airmail postage. Very normal. Indeed, the "AIR MAIL" handstamp might have been struck onto the stamps, but it would not be considered an overprint, a change of category, nor be something to catalog. Is this closer to what you are thinking?
Add: it would still be interesting to see your stamps to complete the thread.