Angle between pinion and shaft
That end of the driveshaft looks pretty beat up to me...as if that end vibrated out and lost a u-joint at some time...or...someone had a hard time installing the u-joint...
On the rear gears...(I am no expert, here...) but the numbers look normal for a 4.10 gearset...E5TW DA is part of the ring gear number...it has 41 teeth and the pinion has 10 teeth. That is the numbers you see on the ring gear...
other stuff on the pinion may have to do with the shift at which it was manufactured and a partial part no# D3TE A...and in my opinion if the pattern looks good then the backlash is fine.
Sometimes folks will grab the yoke and twist it from left-to-right and call that slack the backlash...not entirely true...to get a backlash figure you have to immobilize the pinion and move the ring gear up and down with a dial indicator attached to the housing and the plunger against the gear.
Unless you have a lot of wear on the pinion yoke from a previously loose and/or tossed u-joint...I would not blame the rear...
Concentrate on finding the imbalance in the driveshaft assembly...check the slip yokes, wear in the TFC extension housing bushing, whether the driveshaft was welded together straight to begin with, method of balancing, ...that sort of thing is what I would be eyeballing closely...
Just my .02