Dumb question: Is the transmission fluid level correct? Not too high or too low?
A delay in gear engagement of up to 5 seconds is considered normal if the truck hasn't been driven for awhile due to transmission fluid draining back from the torque convertor to the transmission pan. Presumably it takes a few seconds for the torque convertor to refill with fluid when the transmission is placed into gear. According to the service manual, if delayed engagement exceeds 5 seconds, then:"inspect pump bushing for wear. Replace pump house. " But you're saying reverse is fine and only drive is affected, so that would seem to rule out a fluid drain back issue.
When this condition occurs, have you tried putting the gear selector into 2nd or 1st to see if that makes any difference?
John L.