Ken sez,  what about processed foods...
>If the ingredients are all-paleo
...

I am trying to imagine what these would be.  I have the
disadvantage/advantage of being very overtly grain sensitive.  I can get
sick from licking a stamp or using the "wrong" toothpaste.  Consequently,
I have learned the hard way that if it is processed, it's almost
certainly got some kind of grain protein in it, even if only in a minute
trace amount.

Now, I don't expect everyone else to be as hard core about avoiding very
low levels of such stuff as I am.  However, I'm here to tell you that if
you really want those proteins 100% out of your body, as opposed to
99.99999%, you can forget any kind of processed foods.

As with any of this stuff, you have to decide for yourself how far from
the standard dietary norms it is personally worth it to you to go.