Hi Jeffrey. Yes, you can do that. You’re correct that you should use one form on every page. And in order to redirect to some specific page after submission depending on the page, I recommend storing the page ID or the slug of the page in a custom field on the page where the form was embedded. At that point, you will be able to pull information from the custom field, into a form field, then use that in your confirmation redirect.
If you can use a custom field in the main pages (where the form is embedded) then you can populate a hidden field in the form with the {embed_post} merge tag.
For example, give the main page a custom field with the key “redir_url”. You will need what to decide to use for a value. This can be a page title, page URL, page ID or page slug. Let me know what you want to store there, and I can help you with the confirmation redirect to that page.