Create "virtual" display for use with remote desktop

I frequently use Remote Desktop to access my home iMac from my university campus (using a 13" MacBook with resolution 1280x800). The iMac has two displays, the built in 27" 2560x1440 display and an external 1920x1080 display. There are three issues:

1. Scaling down the resolution makes everything small, or I have to do awkward/annoying panning. I typically only view the 1920x1080 display over Remote Desktop, but even then it's sub-optimal.
2. Large displays require high bandwidth. This isn't an issue if I'm at a proper WiFi network such as my university campus, but occasionally I also use my phone's tethering connection.
3. Everything I do over Remote Desktop can be seen in person on the real displays.

Proposed solution: Somehow create a "virtual" display that's 1280x800.

1. It's the same resolution as my MacBook's screen, so it won't have to scale.
2. It's smaller, and will therefore use less bandwidth.
3. It won't be a physical display, so it won't be visible in person.

Now, is there any way to produce such a "virtual display"?

You could use the Session Select feature of Apple Screen Sharing service. It allows you to log in into a "virtual" user session without showing anything on physical screen. To do so you should:

1. create second user account and log him in "physically",
2. connect using Screen Sharing to your iMac with your PRIMARY user credentials,
3. Screen Sharing will provide you with 2 choices: "Share" screen with current physical user or "Log In" in a "virtual" session,
4. select "Log In" and here you are: you have a "virtual" screen not visible to current physical user.
5. You can now change screen resolution to match your MacBook's screen.