It goes on a monopod head and tilts left or right, works like a champ for either orientation. No need for a big L bracket for me.
Most tripod/monopod heads can drop to a 90-degree orientation, with a full tilt feature like the head you link, or a drop-notch on a ballhead. The issue is that when in portrait orientation, the center of mass is not directly over the axis of support, meaning you're fighting gravity which can lead to instability (and with a monopod, fatigue since you're supporting more of the weight). The 'big L bracket' has the advantage of keeping the mass centered.