Well, that's a critical constraint, no? If there's no minimum off-time then maybe all you need is a big capacitor, the size of which would depend on the responsiveness of your control system.
But now I see that you want power all the time for control, so you need _some_ battery?
Is it possible your electrolysis system draws current depending on the applied voltage, so maybe something as simple as hooking the solar panels up to the electrolyzer will automatically generate (hydrogen?) according to the available power, and you don't need to jump through all these hoops. There are, for instance, solar pump controllers that'll optimize panels and loads automatically...
If there's no NDA, can you share the manufacturer, model, specs, etc for this electrolyzer?