Don't panic - remember, your email is not your system. Your email is an inbox. So just because your email is in 2 places doesn't mean your system has to be in 2 places.
For the last 10 years or so I have carried a personal laptop computer to work so that I can use the organizing software I like on it. (Started years ago when I was using Packrat.) I have LotusNotes at work, I am told we are going back to Outlook soon, and I have my GTD system set up in Outlook on my laptop.
Yes, it would be nice if I could make my work email come straight into my system, but I don't have too much trouble working around that.
All reminders are on my lists (no email folders serve as the reminders although they may hold the action support material). I use the GTD Addin on my laptop and I process all incoming email to a task list and those tasks are automatically linked to the original email. When I am processing my email at work, work-related reference material is stored on my work computer. If something came in (rare) that I thought I would need outside of work, I would email it to my personal email account. My actionable emails I can delete, delegate, do, or defer. If I am going to defer the action, I will either put it into a project email file or in my @action folder on the work computer. But the next action goes on my laptop system. If the email is stored in the email action folder I note "EMA" in the next action and the date so I can easily find the email and refer to it when ready. To get the next action onto my laptop, I can either turn around and type it on the list, print the email and throw it in my inbox for future processing/entry (marked EMA, with the email moved to action folder), call Jott and have it show up in my tasks via voice recognition, or I could forward the email to my laptop (only if it does not contain proprietary information) for processing.
Another alternative would be to keep your lists in a paper format or in some other format that you can carry on a USB drive.
And another - would you be allowed to use a web based system from work?
Good luck!