Got that image. A small key (vintage) model might work much better, though they are only available in 25-27 key vintage melodicas (except for the very first Pianica 32). My favorite is the Suzuki Study II 25, whose praises I keep singing.
Have you tried holding your melodica as Jon Batiste does, so that the weight of the instrument is where the strap meets the back of the four fingers? or as Lowboy sometimes does, with the spit valve end of the melodica cupped in the left hand and the mouth piece propped against your mouth?