Why would you need the monitor to be in portrait mode? Most Vita games play in landscape mode, only a few use portrait like Pinball Arcade, Zen Pinball, and Sunflowers. And even the pinball games default to landscape, so almost no Vita games run in portrait mode by default (Sunflowers is the only one I can think of).
The monitor (my secondary one) is in portrait because that's how I use it for my PC. I would just be fine with the vita output taking up a small rectangle in the middle of the screen. I doubt it can do that, though.