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UPDATE PART 2:
I have been waiting for it to get REALLY cold so I can bring it in since it's worse when it's below 25. In the mean time, I did some research and found a "special service message" put out by Ford. The text is below. I will post the results when I have them change the fluid with the recomended type...
18376 1999-2005 F-SUPER DUTY/E-SERIES/EXCURSION WITH 4R100 - REVERSE ENGAGEMENT STALL IN COLD WEATHER
SOME 1999-2005 F-SUPER DUTY/E-SERIES AND 2000-2005 EXCURSION VEHICLES EQUIPPED WITH A 4R100 AUTOMATIC TRANSMISSION MAY EXHIBIT A COLD WEATHER REVERSE ENGAGEMENT STALL. THIS CONDITION MAY OCCUR AT EXTREME COLD AMBIENT TEMPERATURES WHICH CAUSE INCREASED FLUID VISCOSITY, ALLOWING THE TORQUE CONVERTER CLUTCH TO ENGAGE DUE TO INADEQUATE INTERNAL OIL PRESSURE AT ENGINE IDLE WHILE THE VEHICLE IS STATIONARY. TO SERVICE, REPLACE THE EXISTING TRANSMISSION FLUID WITH MERCON SYNTHETIC MULTI-PURPOSE TRANSMISSION FLUID (XT-2-QSM).
EFFECTIVE DATE: 01/19/2005
My 2000 dually does this as well.... shifts into Drive quickly, but going in to reverse, it takes 1-2 seconds before I feel it engage, and then it is just fine. Does this every shift into reverse, warm or cold.
I'm planning to upgrade to a BTS valve body soon enough, so I think that will probably have some effect on it.