Solved. I dug deeper into the settings and found a way to turn this off under General.
I found an extension called: Page Links To .. does exactly what I needed.
Disclaimer: Although this might not be all inclusive for all form elements, it certainly works for the standard form that comes packaged with Contact Form 7 v2.3 (latest release as of this writing).
Problem: The spinning arrow will not stop on submission and no mail is sent. Seems to be related to the jQuery calls and interference.
Solution:
Open file:
/wp-content/plugins/contact-form-7/wp-contact-form-7.php
Edit line (around 46):
Change this:
define( 'WPCF7_LOAD_JS', true);
To this:
define( 'WPCF7_LOAD_JS', false );
