Which is basically where I am coming from on all this - as far as I can tell, the two do not function with each other. Needless to say, the Rogue saw a natural combination in extra sneak attack dice with an ability which ups the damage per die.
I am curious if the items were written deliberately to exclude the other, or if it simple happenstance of the wording.
You can't get two sneak attacks and +2 to all damage dice on both sneak attacks, but you can absolutely get two sneak attacks and the extra damage on the second one. I'd say that's probably by design, yes.