I’m not sure if you’ve ever heared about Test Management, but your approach isn’t like this.
Just one point to mention: A fool with a tool is still a fool.
A probable way for you is to create a test plan with a one dimension configuration. Create a Run for all your cases and a configration for each of your user (name it like the user).
You will get 200 runs with the same case instances (if you don’t reduce edit them afterwards).
Later you can report on plan level. Although the figures are lousy IMHO.
If you don’t like configuration, you can still re-run an existing run, which will create a fresh copy of your run (nobody say, it has to be used already before). Create manual 199 copies and name them by user - probably as part of a plan.
Or, as mentioned by @BGanger you can use the API as well to create the multiple instances of test runs - isn’t such complicated if you ever have used an API like this.
In general and IMHO only, a lousy test strategy.