Do not ever, ever, EVER cold press with espresso ground coffee. Fine grounds = varied and unpredictable extraction times. Use coarse grounds, in room temperature water, sitting at room temperature for 12-24 hours (depending on roast), and press/filter as soon as finished to separate coffee from grounds (grounds are bitter; **** that).
I haven't brewed yet (SOON), but I've worked with coffee for most of my "job life," and I can tell you--you want results, and you want a standard.
Also, have you considered using coffee that's NOT espresso roast? Espresso is a boring, half-assed roast, only made to seem less boring by horse **** roasts like French Roast. Maybe try and dark, dark Mexican Origin or Papua New Guinean Origin coffee--dark, strong roasts on those--spice and texture: not the bland, boring espresso taste that everyone fawns over (unnecessarily).
However, ******* coffee critiques aside, Cheers and good luck! Let us know how this turned out and how you racked. I may be trying something soon in the very near future