Very interesting idea (the invisible captcha approach)! Since you are a contributer, can you tell us how efficient this strategy is? I mean, do you still experience advanced bots being able to still act as humans?
You can take it one step further and check how fast the form was submitted. If it is below the predefined threshold, it is probably a bot.
[0] To hide the form field, you can use one of these snippets, interchangeably:
"display:none;"
"position:absolute!important;top:-9999px;left:-9999px;"
"position:absolute!important;height:1px;width:1px;overflow:hidden;"