You're right the submit with a module is a bit more difficult because form submits have to go to a URL. It is messier to have to write a component just to accept the input from the module too.
Because of this issue, in Joomla 3 is Matt Thomas wrote a component called com_ajax. Com_Ajax is a component that is designed to assist modules with doing things with modules when there wasn't a specific URL to work with like you have in a component.
Your case to me is exactly what com_ajax was designed to help deal with. Here's some documentation on using it:
Then in your helper you'll set up the class for the module:
You will set up with getAjax() method:
To handle pulling in the form submit data via JFactory::getApplication()->input()
You will then return some sort of response, probably something like a JSON string which is a success or error message.
Hopefully this helps!