Not sure of your setup, but a those that have made a successful "hill" in a pot did so in a wine barrel cut in half. They need that much dirt to thrive, and after the second or third year they will probably outgrow that. They put out a LOT of roots.
As far as growing on an apartment balcony railing, I would have to advise against it but I bet in a big pot you could make it work with daily care. They want to grow towards the sun(vertically) and commonly reach heights of 18+ feet. People have trained them to grow horizontally through a chain link fence, but they have to train the bine daily. A two lb. harvest would come from a second or most likely third year plant with optimum conditions. My five year old here in michigan reached 12 feet by June 6th before the growth tips were torn off in a storm. Obviously nowhere near perfect. I got 3 oz. of dried hops from that plant.
One more thing, they really like full sun. Can't really tell from your description, but even 3/4 of the day will drop yield.
All this said, if you plan on moving somewhere with a yard and can get a giant planter I'd definately recommend putting in a rhizome. Just think about it like planning for the future. Even if they don't produce much, if they break ground and grow they're producing a root system that can easily be moved to a permanent location and will already be mature enough to produce your 2 lbs. the first year it's there. It's like a hop starter.
