Hi 7storiesdeep,
I don't know if you figured out the problem but I finally got it the Contact form 7 to work after talking to Dreamhost. Dreamhost has a policy that you have to have an email address set up with Dreamhost and this is the address that you have to put in the "From" box in your settings for the Contact 7 plug-in. Who would have guessed? Anyway, to create your new Dreamhost email address go to this link below and then enter the new email address in the settings.
https://panel.dreamhost.com/index.cgi?tree=mail.addresses&
(Panel > 'Manage Emails')
Hope this works!