In the case of the Mac, I would have to suggest that you just be patient.  I am not familiar with the Windows Phone Connector, but the reported "force" of disconnecting the internet connection while checking for updates is a Zune workaround, not advertised in any way to work on a Mac. 

It is not Verizon who is holding back the update.  Microsoft had announced in the beginning that they were going to roll it out in a controlled fashion, with only 10% during the first week, and ramping things up if they went smoothly.  Things DID go smoothly, and they have ramped up, and from what I have read, at this point the update is available to about 50% of Windows Phone users.  As reported by WPCentral, after ten days, 20% of users are running Mango.  Compare that to 38% of Android users being updated to Gingerbread 10 MONTHS after the update was released (http://www.wpcentral.com/just-ten-days-microsoft-has-updated-20-phone-mango-world-wide-android-weeps).  Microsoft is well ahead of that curve.  Remember - they have said that they expect everyone to have Mango available to them by the end of October.  I know it is hard to sit and wait while your friends are using Mango, but I hope this helps you.