Right-click in the Playing Now window and choose Detach Display. You can then drag the detached window onto your case monitor. That's assuming your built-in case monitor functions like any other monitor where you can drag-and-drop windows between monitors.
If you double-click on the detached display, it will maximize to fill the screen. I can say firsthand this works (on my 2 TVs) for cover art, artist images, built-in visualizations, etc. As for VST's, I have limited knowledge. But I believe VST's are shown within the DSP dialog, right? If so, activate the VST in the DSP dialog and drag that dialog to your case monitor. You can maximize the dialog to fill your case monitor's screen too.
Hope that works for you.
I guess I should note, you will have to repeat Detach Display process with each new MC session. But as long as you don't close MC, you can show whatever you want on your TV, and detached display will remain unaffected on your computer's case monitor.