I'm sorry for the rough language, but this "feature" is one of the most retarded features that Stack Exchange implemented in years. I rarely use the mouse, and equally rarely use the GUI file manager. Removing the idiotic hotkeys that otherwise prevent normal text editing is a huge pain as it is, now I need to combat this idiocy too?
The dialog box was recently redesigned, but the functionality hasn't really changed. If you have an image in your clipboard, you can use Ctrl-G to bring up the Imgur dialog box and paste the image using your OS's paste-from-clipboard keyboard command (often Ctrl-V or Command-V). No need to use the mouse or the file manager.
If you already have an image hosted somewhere, you can also use Markdown to link to the URL:
![New Imgur uploader](http://i.stack.imgur.com/qag6ht.png)
Malabarba has a rather fine Stack Exchange mode for Emacs, but it does not seem to support image uploads just yet. Perhaps it could provide some relief to your hotkey annoyance when composing posts?