What is this "tremendous amount of extra mass" you are referring to? If we take Hindenburg(not -berg you millennials!) as an example, the solution, and the idea, would be just to replace gas contents of the space between hydrogen cells and the airship outer shell.
This is not increasing mass a lot since the only thing needed is to have a airtight and controlled outer shell where the pressure can be adjusted. Splitting the sections and adding pressure monitoring system would detect the outer shell ruptures immediately, adding time to react and repair damages if possible.
All this does not make the airship fire or accident proof but it would add one very good feature: a spark or a hot spot of heat inside the outer cell would not ignite the hydrogen cells, specially if instead of nitrogen we use helium as the "insulator" gas. Then there is no oxygen for any kind of fire. Any total puncture would result a hydrogen+helium leak. I don't know how they dilute but my guess is probably better than hydrogen and nitrogen.
Point here is that making the hydrogen relatively safe as a lifting gas it would make safe enough autonomous airships. Those can be used for transporting cargo and other tasks which do not need any personnel on board.
Of course it is possible just use hydrogen only and take all of the risks at once... but still I'd estimate that cargo shippers would like high payload and added safety.