Is there a way to invalidate script parameter cache other than login/logout?

Script parameter cache? Not sure what that is. Are you using the N/cache module or referencing the script object's deployment parameters?

When a user logs in, script parameters of type Company are cached by NS. If these values are changed by another user then all other users continue to use cached params.

use N/config instead

^^^ Yes, use N/config and load the companyinformation record to get the value.