When viewing the ships, we have four things to consider.
1. The balloons are too small for any normal gas to make the ships buoyant.
2. Ships fall slowly even when the balloon is broken, so the balloons are not creating the bulk of the buoyancy.
3. Balloons deflate downward instead of upwards, meaning the gas itself is not buoyant.
4. The ships all have a lot of very hefty metal parts.
My original proposal was that the gas inside the balloons does not matter, and it is a special machine (the balloon fixpoint) and the actual shape of the balloon that creates the ship lifting force. I am abandoning that thought. On the other hand, I am sticking with the hull machine (which consists of all the random gears and seemingly pointless pipes and pistons around the ships), creating almost neutral buoyancy, since the ships do fall slowly even when the balloon is broken. The weight of the massive amounts of metal is negated by the hull machine, which only effects metal to a great extent and makes it 'buoyant' to surrounding air. A wood ship, or anything not made out of metal, would have a much lower, if any, effect.
So, what is causing these effects? I have abandoned my balloon shape thought in favor of a silly idea from a movie. This movie being 'The Absent-Minded Professor', and the idea being Flubber. The hull machine is literally the flubber machine from the movies, only giving neutral buoyancy to the metal of the ship structure instead of full motion. Since the hull access point is mostly pipes, I would wager this material is a liquid. So, how does this apply to the balloon?
There have been mentions of 'balloon gas" at several points, and adding hydrogen somehow damages the balloon while giving it much higher upwards force. The green gas escaping from the Chaladonian ships is said to be an advanced or concentrated version of this gas. This means the balloon does not contain hydrogen, nor any known gas, but adding hydrogen makes this gas more effective. So, the GOI Universe is obviously using some sort of gaseous version of the the hull machine 'flubber' in some way. However, it can not be using the gas itself for lift, since the balloon sags when damaged. This sagging effect may come from the gas inside shrinking, rather than escaping.
This would explain the Mobula balloon collapsing upwards because it is attached to the top and must pull upwards as the gas inside shrinks. This would also help explain why the Mobula does not tip over, since the hull metal itself is almost neutrally buoyant, and the balloon does not actually produce lift. The turbofans are there just to stabilize the ship's forward and backward roll while changing directions. Some ships may be using some helium in their balloons for stability, like in the Goldfish or Junker. They have larger balloons over the ships, and adding a positively buoyant gas would keep that end up. There could be smaller helium balloons inside the main flubbergas envelope.
So, perhaps the 'flubber' liquid is even more powerful in gas form, and can be used to precisely control vertical movement. Increasing or decreasing the mix in the balloon adds to or subtracts from the strange buoyancy force effecting the metal on the ship. This makes sense from the game sounds as well. Going up makes a hissing sound of adding gas, while going down produces a pump sound of pulling gas out. Adding hydrogen is a catalyst that increases this force by quite a bit, but also reacts with it. Basically like turning oxygen into water by chemically bonding it to hydrogen.
The design of all the Alliance ships supports this mechanic of massive metal ships being held aloft by small balloons in odd places.
The original Icarus was made mostly out of wood, and had a huge balloon, so did not use this technology to great effect. He likely did use hydrogen or helium in his balloon, and a rudimentary hull device.
