It would be great if you could screw some conduit clamps like these to the railing to hold a mast if the landlord will allow it or lay a mast against a vertical hand rail and get hose clamps that will go around the railing and mast. Or use conduit clamps to mount a mast to a 2X4 that is as long as a vertical rail and C clamp that to a vertical rail. I've even used huge Ty-Raps to hold a mast to hand railing for temporary use.
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I can't believe you're not on the air yet. Don't make me drive out there and do this.