Here is a photo of me holding the melodica in one of the basic playing position and using a melodica apron. In this case, I am using one finger on my left hand to hold down the high G. I really like to accent chords on occasion by punching them while holding down a high note with my left hand.
As noted before, once in a great while I will use my chin to hold down the low F as a drone or accent note. Note that this melodica is a Piano 27, not a Piano 26. Both work fine.
It would seem there is one disadvantage to playing this way. The throat is bent and not as open as it could be. So far, I can hardly tell the difference between this position and a heads up position as it relates to air flow and diaphragm techniques.