Champagne shall be your model for pressure fermentation. I dislike the time it takes, the risk of rotting, the doubtful reproducibility.
Air is the cheapest and most available gas. I suppose a reliable valve (not for bike tyre) per bottle is too expensive.
The only way I see to use the original caps that fit the bottles is to operate at depth in the lake. 5m for 0.5bar overpressure, this is difficult in apnoea, feasible with oxygen.
Many processes become possible then. With diving bottles, expire your air in the bottles, close them. Or pump air from the surface through a pipe. Or bring air to the depth in more bottles, fill some while emptying others.
The bottles should be ballasted. I'd sink and raise them with ropes. A funnel helps transfer the air.