The fine young gentleman from the country I am attempting to visit informed me there is nothing he can do push the miles quicker. He did, however, extend my hold until July 1st. (The flight is on June 30th) Ha!
Regardless, I pried for information as to whether the miles may process faster than 48 hours. He passively indicated that its possible. I have little faith.
The internet seems to indicate they process within 24-48 hours. My cut off for comfortably booking this flight is at the 38 hour mark. Perhaps I will fall ...-backwards into the direct flight at 8:30am. Regardless, I am the epitome of a flexible traveler. At this point I'm sealing this one for the Google archives.
Afterthoughts? Thanks everyone.