Reich
Back your phone up to iCloud (this is probably the biggest bottleneck if your data doesn't fit into the free storage). If you have a recent backup, you can wipe your phone (Settings -> General -> Reset -> Erase all content and settings). That should clear up plenty of space on your device. Then upgrade and restore your backup once it's completed. This is how I upgraded to iOS 7 and 8 without having iTunes installed. But definitely be _sure_ you have a backup.
Although, I will say it does not sound feasible, but I would love to hear an expert has to say.
Easy enough to change in system preferences, though. And with using Vim NERDtree, or some other directory plugin, it makes sitting at the top level directory of your project, with multiple projects in multiple tabs, pretty easy.
Are you on Mac? If so, have you done anything to make tab-switching easier/faster? I'm interested because I only recently set mine up this way, and am always open to more efficient methods.
It also just sounds like there was a bad experience with a particular tech support rep, who may be new. In my experience, these issues are ALWAYS exceptions to the $20 fee. If the 'standard' workarounds don't fix it, they will escalate you to a supervisor and put in a ticket with engineering who will resolve the issue within 48 hours.
Maybe OP will see this and give their tech support another shot. If not, the token expires in about 28 days.
*This information is less than a year old, but rules may have changed.
I know a lot of people are saying that this shouldn't even have to be a step when you switch phones, but the fact is that you chose to use iMessage for the features. It could have been turned off at any time, they are not forcing you to use it.
It would be great if there was a way to fix this without having to call (or unregister your phone number from your apple id), because of not being able to know that it's happening. But it's not like Apple is deliberately trying to keep your messages hostage. Besides, you've already switched phones.