Simple Question:
Why not go to or call the local alien registration office and ask for an extension ???
If they know what your intentions are they will appreciate it and most likely give you an extension. Can´t imagine too much fuzz about it.
Just give them a call beforehand and inquire !!!
If they agree bring along a confirmed reservation for your flight to the U.S. as it will certainly help ease the office clerk´s decision in favor of you ... !

Btw.:
Regarding your "non-existent passport stamp" ...
As you may have a machine readable passport you won´t get a stamp but your arrival/departure dates will be recorded !