You'd have to think the free gas and the gas in liquid is...

You'd have to think the free gas and the gas in liquid is in equilibrium under the cap... so if gas is extracted will it release the suspended gas to replace what's extracted? Or will the water rise and fill the void? I'm thinking the former as the it's not a sealed pressure vessel down there so the water table is sitting at its natural height. So possibly adding a little negative pressure into the cap should allow more He to exsolve then it becomes a question of the permeability and the size of the volume that allows that these actions would influence. But it is a cheap repeatable process to duplicate at different locations.