Ellis offers a vertical forge.
I am in the process of building a couple of different gas forges, both vertical.
I have a casting furnace used to melt aluminum, copper, and brass, so my belief is that the vertical design wins on efficiency.
Should reach welding heat very quickly, and forge welding is much smoother not only because of improved efficiency but also the floor design does not seem to be as critical. Kitty litter, easily replaceable floor, or what have you, the floor in a vertical is simply not as critical as a horizontal.
A few people have even let the flux drain into a stainless pan underneath!
Most people do not like the idea of dropping work into the forge; one of the verticals I'm making will have a shelf much like the plynth on my casting furnace. Don't yet know how well it will work, but I'll certainly find out.
I can see where the "hot handle" can be a problem, but to me a small fan next to the door is not too much of an inconvenience.