One thing worth considering is going back to hydrogen as a lifting gas. Not only is it a better lifting gas than helium and much cheaper, it could be used as fuel.
An airship that burned its own lifting gas would have the curious property of getting heavier the further it traveled. This could be countered by dual-fueling it and also have engines that burned heavier-than-air fuel like kerosene or propane. The hydrogen engines could burn the lifting gas at the same rate as the kerosene engines burn the ballast-fuel.
That article mentions that the Zeppelins experimented with burning Hydrogen lift gas as fuel "without much success" but doesn't add detail.
[1] https://en.wikipedia.org/wiki/Blau_gas
[2] https://en.wikipedia.org/wiki/Buoyancy_compensator_(aviation...
I'd expect that, like a lot of problems zeppelins had in the 1920s, burning hydrogen would be more feasible with modern technology.
I'd also point out that the thing that made hydrogen dangerous in those airships was that the skin was two layers. The inner skin was the gas bags, which were very fragile, and then the rigid structure and the outer skin to protect the fragile bags. This was a problem because hydrogen could accumulate and mix with air between the inner and outer skins. The outer skin also was quite flammable. Nowadays, we can make materials that are both strong enough to serve as an outer skin and impervious enough to serve as a gas bag for lifting gas, so modern airships have only one skin and nowhere for the lifting gas to mix with air inside the structure.
But if you aim for a buoyancy-neutral fuel, you can just add hydrogen to the mix, as little or much as you need. That custom blend then would be precisely the thing you don't invent a creative name for but just use a color code ("the blue one").