Even here in CA on a cold morning (45F) my tranny is stiff going into 1st and 2nd until it warms up...
May be the nature of the beast.
Be careful using full synthetic. Sometimes it is so slick, the syncros won't grab and you'll grind shifting gears. You can get synthetic for Posi/LSD's. I would go with that.
White 96,4x4 w/Y2K motor,Warn man.hubs,K&N filter, 3row rad., twin 16" electric fans w/SPAL FAN-PWM, 1.4" body lift, 4" UPYOURKIA lift kit,265 75-16 TREADWRIGHT GUARD DOG TIRES ON 16" DC-2 wheels, 140 amp alt. dual batts.