Based on the pictures you posted, I would say that your truck does not have the milkshake I am sure of that.
I would work on figuring out that wine, I also believe that it isn't the transmission, change the fluid (all 16 quarts) to see about the shift hesitation.
Is your radiator visibly newer than the surrounding things? That would be a sure sign of past 'milkshake'
That wine sounds bad, but could be any number of things related to the engine. Start by disconnecting your accessory drive belts 1 by 1, see if it goes away. Obviously don't run the car long with them un-hooked. That or get a mechanics stethoscope and start poking around to isolate the noise.