Long story short:
Don’t use files to exchange this data. Use services.
To get contacts from Outlook (Exchange) into iOS, I used the macOS-native Contacts app. I connected to the Exchange account that had the contacts needed. Then I connected to the empty iCloud account. I selected the Exchange account, selected all of the contacts, and dragged them en masse to the iCloud account. In a few minutes, all of the contacts appeared in iCloud with the correct data in the correct fields. A few minutes after that, they were on the destination iPhone.