I just wanted to add an update and conclusion/solution to my issue.
I saw another post with a user having a similar 404 error (nothing happening upon clicking “submit” on the widget sign-up form) and apparently their custom theme didn’t have the <?php wp_footer(); ?> code in the footer. So, out of curiosity, I checked the theme I was using and it wasn’t there, so I threw it in and now it all works great. Phew!
Thanks.