For reference, I have first checked other questions/answers including: Questionee? Inquiree? Interrogatee? (and it's listed "possible duplicates") but those are in reference to the user rather than the survey associated to the user.
Breaking it down, a survey by itself is just a template used for retrieving individual responses. Once the survey has been copied and served individually, it has become an instance of that survey. "Response" and "instance" are too ambiguous for referring to an individual survey specifically. "Surveyee", "inquiree", "interrogatee" and "questionee" are more specific but they refer to the person/user/subject who started/completed any number of surveys and not their unique set of answers for one in particular. If I have a pile of unassigned surveys and a pile of assigned surveys, I would refer to a random selection from each pile as "a survey" and "this person's survey" respectfully. It is the latter I wish to identify as a single, unambiguous noun.
All I have been satisfied using thus far in my (web) project is 'survey-instance' (hyphenated for URL compatibility) but I cannot shake the thought there is a better, single-word descriptor.