Thanks Wayne & Hilmar:
What I ended up doing was to re-write my Delphi app to get it's screen print from the clipboard, instead.
Since API_APRUN creates a new thread, it's possible that the app it spawns is ready to retrieve the
image from the clipboard before VFP has finished putting it there. I added an inkey(1) before I create the
API_APRUN object and now everything works great.

Mike