There is no endpoint in the API that will give you user_info objects across the network.
The two end-points you've found is the way to go:
- fetch all associated network_users for a user
- call for each network_user per site /users/{userid} to collect the user_info objects for the other sites the user has a profile for.
- combine / merge the data you've fetched for your goal.
See also: Getting global information (Stack Exchange) about a list of users