In light of my current workload, I am unable to develop a recent idea and present it here for whoever will pick up the torch.
For background, you should have a look at this Wikipedia article:
The problem is that the balloon changes buoyancy because it gets warmer/expands/rises during the day and cooler/shrinks/falls during the evening. The project team addresses this by dropping liquid ballast during the evening and (IIRC) purging gas during the day.
They made it 90% of the way across the Atlantic before running out of ballast. That's really cool.
It occurred to me that dropping ballast is really sub-optimal. What you really want to do here is to dynamically change the density of the craft so that it displaces more or less air depending on the temperature. There are a couple of ways to do this. The straightforward solution would be an onboard compressor that can reduce the amount of gas in the flight envelope. This is not a lightweight or cheap solution.
My gee-whiz moment was the realization that you could store the excess gas as water if you use hydrogen. When you need additional gas (in the evening), electrolyze it apart in a split cell and route the hydrogen to the flight envelope.
Electrolyzing water to generate gas should get you more bang* for your pound-of-payload weight than just dropping it.
* - Hydrogen pun.
It's also technically feasible, though not easy, to burn** the hydrogen in a controlled way and recapture the water to allow very long (circumnavigation) flight durations.
**Platinum catalyzed combination with atmospheric Oxygen. Still really hot, but not as hot as a flame. The hard part is that you have to get rid of the heat to condense the steam into liquid water in a pressurized environment. It has to be pressurized because the atmospheric pressure is negligible and the liquid water in the electrolytic cell will boil off.
The open feasibility questions are "does our battery technology permit the energy density required for this?" and bounce it against the Ideal gas law to make sure that a reasonable volume of water in the cell produces a reasonable volume of Hydrogen.
Good luck, let me know if you try it.