Follow this:
0. I'd make a Zone specifically for this use-case, if you will be using this copy of MC in other configurations.
1. Change Options > Theater View > Behavior > Jump on Play (video) to None. This will keep Theater View exactly where it "is" when you pick a song to play.
2. Play a video file in Standard View. It doesn't matter which one. If you made the Zone, make sure you select it before you play.
3. In the Playing Window in Standard View, right click and choose Detach Display.
4. This "pops out" the video into its own separate, resizable window. You can then drag this window over to your secondary monitor, and double-click on it (or maximize it) to make it go fullscreen.
5. It will remember these settings (window position and fullscreen status) forever as long as you don't resize it again.
6. You can have one separate detached display per Zone. They work independently, and you can run them simultaneously.
7. With the display detached like this, when you play something from Theater View, it will automatically play to the Detached Display. Since you set Theater View to not Jump to Fullscreen when you play back, it'll stay where it is, and allow you to browse for something else.