I don’t see how REST adds a constraint that two resources could not have the same value. The resourceType/ID is just an example of the easiest use case rather than the best way to go from a RESTful point of view.
If you read paragraph 5.2.1.1 of Roy Fielding’s dissertation carefully, you will notice that Fielding makes the disctinction between a value and a resource. Now a resource should have a unique URI, that’s true. But nothing prevents two resources from having the same value:
For example, the “authors’ preferred version” of an academic paper is a mapping whose value changes over time, whereas a mapping to “the paper published in the proceedings of conference X” is static. These are two distinct resources, even if they both map to the same value at some point in time. The distinction is necessary so that both resources can be identified and referenced independently. A similar example from software engineering is the separate identification of a version-controlled source code file when referring to the “latest revision”, “revision number 1.2.7”, or “revision included with the Orange release.”
So nothing prevents you from, as you say, changing the root. In your example, a Business is a value not a resource. It is perfectly RESTful to create a resource which is a list of “every business located in a city” (just like Roy’s example, “revisions included with the Orange release”), while having a “business which ID is x” resource as well (like “revision number x”).
For Employees, I would keep API/Businesses/X7N/Employees as the relation between a business and its employees is a composition relationship, and thus as you say, Employees can and should only be accessed through the Businesses class root. But this is not a REST requirement, and the other alternative is perfectly RESTful as well.
Note that this goes in pair with the application of the HATEAOS principle. In your API, the list of Businesses located in a city could (and perhaps should from a theoretical point of view) be just a list of links to the API/Businesses. But this would mean that the clients would have to do one round-trip to the server for each of the items in the list. This is not efficient and, to stay pragmatic, what I do is embed the representation of the business in the list along with the self link to the URI that would be in this example API/Businesses.