How can we integrate a lightweight public ticketing system into our documentation feedback form?
We publish a substantial documentation set online. Each page has a place at the bottom that asks "was this helpful? (Y/N)", and if the person chooses "no" we offer a textbox. We collect all this feedback internally (it feeds into our internal ticketing system, except for the spam), but to the user, it feels like typing feedback into the void -- you never know when there'll be followup. Further, because the communication is one-way, we can't ask people to clarify comments when needed.
We would much rather have a public tracking system for these issues, where the response to the form submission would include a link with an invitation to track this issue. (We'd rather not ask for email addresses; this should feel completely opt-in and safe to the person offering us the feedback.) We want to find a place to host tickets that the public can follow and that we can update (either to say we've fixed it or to ask for more information). I'm imagining that all of these tickets would be created by us (well, by our feedback system) in response to the in-doc feedback, at least initially.
What tools should we consider? Opening our internal ticketing system to the public is not an option.
If we were managing our code (or documentation) on GitHub then using GH issues for this would seem obvious, but we're not, so it feels strange to create a project just to "host" issues for some other system. We're a for-profit corporation, not a non-profit or open-source project, and we don't want to step on toes or give a bad look by misusing tools meant for a different context. We also don't have a lot of money to spend on this and need to keep administration simple.