Using the mini without a monitor

Essentially what I'm trying to do is have the Mac Mini in an always-on state, serving iTunes media, running backups, etc. I don't want or need a phsyical monitor with it as I typically either remote in to it via Screen Sharing or via TeamViewer. The problem is, when restarted, the Mac Mini detects no display and defaults to the lowest resolution possible (not sure why they wouldn't default to the highest, but who knows). When I finally remote in to it, I do not have the option to select a higher resolution because a monitor isn't hooked up to it to display other higher resolutions.

Does anyone know if there is a way to more or less force the Mac Mini to default to a native 27in iMac resolution (2560 x 1440)? I'll even take 3rd party if needed...