Here are two options.

Replace any bio-balls with blocks or course open cell foam. This will
reduce the gas exchange.

Change the chambers so they no longer have air spaces. In the skimmer
place two pipes, one that fits in the outlet with the top an inch below
the top of the skimmer. The second is a larger pipe that is the same
height or a little higher, cut some slits at the bottom of the pipe to
allow the water in. This forces the water down the skimmer then back up
to the higher outlet. You can do something similar in the tickle
portion of the sump although this generally requires modifications to
block where the water is designed to go into the sump. Or just remove
the tickle box and allow the water to go directly into the sump
(probably what I would do). If the skimmer is full of water and the
outlet is under water in the sump there should be no place for air to
get into the plumbing and it will eventually fill with water.

Four plants will not be enough to replace the biological filtration you
will lose, so plan on adding many more plants.