No, there is no way to do this with your Nikon camera. Yes, this is frustrating.

Part of the reason, perhaps the reason for not being able to leave the mirror up, has to do with the historical design of Nikon's aperture control mechanism. Historically, Nikon bodies used a physical linkage mechanism to directly control the aperture. Other manufacturers long ago switched to entirely electronic control of the lens, including aperture.

Before a camera is taking an image, the camera meters the scene with the aperture wide open, to let in as much light as possible for the autofocus and metering system. When the shutter button is fully depressed, the camera stops down the aperture to the desired or set value, flips up the mirror, and exposes the sensor by opening the shutter. After the exposure, the shutter is closed (or returned to ready state), the mirror is dropped to reflect light through the viewfinder, and the aperture is opened back up again.

In Nikon bodies, the aperture control mechanism is linked to the mirror action in a manner analogous to a retractable ballpoint pen. When the aperture is told to stop down to a set value because the mirror is going up, the only way to open the aperture again is to return the mirror to the down position.

To modern eyes, this seems like a horrible design. But remember that before the age of SLRs being capable of taking serious digital video, aperture action didn't really need to be separate from mirror action.†

Nikon has recently started making a push towards electronically-controlled lens apertures with their "E" lenses (not to be confused with the much older—and obsolete—"Series E" lens line). However, until they refresh the vast majority of their lens lineup to adopt electronic aperture control, for the foreseeable future all DX and FX bodies will still also have a physical aperture control linkage to control the aperture of non-E lenses.

† : Don't get me wrong, even as a stills-only photographer, I wish the aperture was separate from mirror action. It frustrates me to no end when taking a bracketed sequence, including when I lock up the mirror and compose in Live View, that the mirror is cycled between each shot, even on higher-end and pro bodies like the D800/D810 and D4.