Death before sin is a problem as well, because death is a consequence of sin.
This is true.
Though I'm pretty sure that plants don't count for 'death' (i.e. man and animals could certainly eat as many plants as they wanted w/o it counting as death; and carnivores eating may not have counted either -- we have to remember that man is special from all the animals, being made in God's image, so even animal deaths* might not have counted [very spotty, but a possibility])... or maybe the Tree of Life was a Hot-dog tree and carnivores ate that. ;)
* -- God's warning about eating the fruit of the Tree of Knowledge of Good & Evil would be even more powerful if there was a carnivore/animal-death ecological-cycle going on in Eden because it would have a sort of "if you do this, you'll be part of that cycle" connotation. (Remember that 'the world' can mean mankind as in Jn 3:16.)
** -- Note I'm not denying the Bible, I'm pointing out that the death of man, any man, is a very significant event; likely much, much more than we know or understand.