That's indeed something you could achieve with Jetpack's Contact form:
http://jetpack.me/support/contact-form/
You'll be able to add as many contact forms as you need, to your different pages, and send the Feedback emails to different email addresses and different agents.
The email address behind the form is never displayed or accessible to spammers or to your readers.
You will also be able to add or remove fields as needed.
I hope this helps.