This could be a crazy idea or a really good idea depending upon your outlook the result of some initial experiments . . . but, you could hold the melodica with your right hand and reach over the top of the keyboard with your left hand, playing the keyboard backwards with your left hand. Many two-handed melodica players provide accompaniment to their right hand using their left hand in this fashion. As a one-handed player, you would use only your left hand.
Jimi Hendrix took a right-handed guitar and flipped it, restrung it, and played left handed. This put all the controls at the top of the guitar and not the bottom.
The great bluesman Albert King flipped a right-handed guitar to play lefty and did NOT restring it. The controls and the strings were kept upside down. (The low E string on the bottom and the high E string on the top.)
Hence, anything is possible.
Whether you could actually get good at articulating passages this way could only be determined by trying it for awhile. This might result in you developing a very unique style and sound: something you may consider good or not so good.