Hi Jeanne, I tried to think of a clever way to do this, but I couldn't come up with something that wouldn't create additional problems. As you note, this is really not what Qualtrics is designed for. I think you are describing something more like a database or CRM...or even just a good ol' Excel file. If you are resource constrained and the data are not sensitive, you could probably set this up in Google Sheets to allow for simultaneous editing. If the data are sensitive, you might do better with a different system. There are probably some free or free-to-you options, like MySQL, Microsoft Access, Microsoft Dynamics, though there may be more of a learning curve.

Hi Jeanne,
You're right that this type of application is a stretch for Qualtrics, but if you've already ruled out the alternative solutions that ClairJ described, there might be a way to do it, even if it's not completely seamless.
First, using an Authenticator might be a dead end. Instead, if you already have your universe of cases in the Excel spreadsheet, you could use the Personal Links to generate a link for each case and copy them into the Excel file. Then you could share the Excel file with your research team to find the appropriate link for each case they are reporting. This would address both your concern with preventing duplicate cases reported, as well as the question with exceeding your response limit.
One way that updates could be made to cases is with with Retake Links. This is where it might be become less manageable. Retake links can only be generated on an individual basis by someone with access to the survey in Qualtrics, so if the volume and frequency of updated cases is high, you would be spending a lot of time generating the links and sending them out (unless the members of the research team also had access to the survey in a Qualtrics account).
Another way updates could be made is by setting the survey link expiration to a distant date, and setting partial response closure to the farthest setting (one year), and having the research team enter the cases but not submit until all updates have been made. That way the same original link could be used for updates; you wouldn't have to use retake links. However, this would not be a viable option if you need to include cases in your analysis that would still be subject to being updated.

Thank you, Claire. This is very helpful information to have, helps reassure me that there isn't something obvious I'm missing. (The data ARE sensitive, some of the information complicated, and quality control is particularly important. Qualtrics is quite appealing for what it allows in terms of skips, display logic, defaults. But there is a trade-off, to be sure!)

Matthew,
I like the way you troubleshoot! You have definitely given me some lines to pursue. This may be inelegant, but it still holds promise.
Thank you.

(People: I welcome any suggestions, however farflung. The answers also help me better understand Qualtrics limitations and strengths.)

The solution from MatthewM is about as good as you are going to get, I think!
The only thing I'd add is that instead of using unique links, you could set up links that pass the case information into the survey
Passing Information via Query Strings | through the link. This would solve the issue of links expiring (as these can be reused), but creates problems related to the number of responses getting out of control and also having multiple records for each case. I think you'd have to actively manage your dataset, deleting old records when an update is submitted.