Hi, just a little feedback. Under conclusion, you write:
If the SQL Server Browser service is not running, connection strings will have to specify the port number in order to connect.
As I understand it, this is partially correct. You do not have to specify port number if the server is listening on port 1433, as it does on default instances by default. Apart from this, it is correct, whether you have specified port numbers manually or not.
The SQL Browser service is only for named instances. If you change the default port of the default instance, you will always have to specify the new port number on client connections -- the browser service will not help.
For named instances, if you disable the browser service, then yes, you will also have to specify the port number. For named instances, if the browser service is enabled, then you won't have to specify the port number no matter the port number chosen in the SQL Configuration manager.