I just got a 1919 Conn mellophone. It’s not your modern marching horn with the front-facing bell, but the old French-horn shape, but (of course) with valves for the right hand.
Now my dad, who used to play mellophone himself as a kid, said “Don’t put your left hand in the bell; wrap it around the valve casings to hold the horn.” The thing is, his valves were straight up and down and the casing was easy to get hold of. The valves on my Conn are angled so that the caps lean to the left, forcing one to play the horn at an angle like a backwards French horn. The casings are packed in alongside tuning slides and awkward at best to grab, and the angle of the valves means the left hand and arm would have to be forced unnaturally away from the body to do so.
So is this one mellophone that’s actually meant to be played hand-in-bell?
Here is a picture of an instrument like mine.
What a neat instrument. It certainly doesn’t look like the left hand is supposed to wrap around the valve casings. I can’t even see how you would do such a thing. Of course, with the mellos that we use, the left hand actually holds the weight of the horn via the valves. It’s like playing a fat trumpet. Your horn, however, doesn’t seem to have that in mind.
My guess is that one would put the left hand somewhere in the vicinity of the bell. However, it may not be needed in the bell, the way a true horn player uses his/her hand. This instrument strikes me as something a session musician would use in a stage-musical or some other variety performance. With the alternate slides, the player can quickly jump from one sort of arrangement to another.
Does the horn play? How does it sound? My guess is that it has a bright sound. If you have a child, tell your school’s band director that you absolutely insist that your child play this horn in band and watch the teacher’s reaction. 
We used mellophones with front-facing bells in my junior high stage band, to fill out the trombone section. There were only two trombone players in the school, and you kinda need four for a big band.