Re: ...helium currently comes from natural gas..."
Hydrogen is better than helium for balloons in just about every way. It's lighter, providing more lift; the molecules are larger, meaning they will take much longer to leak out of the balloon; it's way, way cheaper and easier to produce; and unlike helium, the supply is a renewable resource. As for the fire thing - it was the fabric of the Hindenberg that burned, the hydrogen was incidental at best.
The only reasons not to use it are (1) it's a bit dangerous to store (much like any other explosive fluid), and (2) there's more profit in selling helium.
What bothers me about airships for long-distance transport is the speed. If the ship manages an airspeed of 60 knots, then a gale force or stronger headwind means your ground speed will be zero or negative. I've found it hard to find decent data on the subject, but from what I have found it looks like in the upper troposphere, wind speeds are at least that fast fully 25% of the time. That's a lot of downtime.