I copied your Add to Cart button code out of the post-form-submission page and pasted that into a test page, where I confirmed that code worked fine outside the context of your page, so that rules out any issue with your product settings or the button code itself. Whatever the source of the problem, it must be something in your page interfering with the normal operation of cart buttons with menu options.
Add to Cart button codes without menu options are just linked images, whereas the code with menu options are actually an HTML form, where the button is an <input type="image"> that submits the form to send the selected menu option value to the cart. I wonder if scripting in your page that catches your registration form submission may also be intercepting cart-button form submissions as well, so clicking the cart button gets as far as displaying the cart overlay in your page, but then the cart doesn't have any actual form-submission data to work with.
I'd suggest bringing this reply to the attention of whomever set up your page, which should point them in the right direction to sort things out.