In General Qi Jiguang's book, his Long Saber stances came without any explanation on how they are being used in an actual fight. Here's a quick 3 mins video that I've made to share my interpretation / theory on 3 of the stances, which actually looked very similar to each other.
3 things that we need to establish:
Firstly, we assume that there are no redundancies. Each stance has its own unique purpose and techniques in it.
Secondly, the Long Saber wasn't drawn to scale. The overall length should have been 6 chi 5 cun, which is almost 2 metres long.
Thirdly, the portion above the guard has an approx 30cm bronze fitting, which allows you to hold onto, and expand your grip. This allows you to use it like a Polearm or Spear. Below is an example from the Korean's reenactment of Muye Dobo Tongji, which is based on Ming martial arts manuals.
When you're using a sword, both of your hands are typically closer to each other. This allows you to change your striking angle easily, so that you can make different types of cuts from various directions.
But when you're using a Polearm, your hands are further apart. This gives you better structural stability, meaning someone will find it difficult to push your weapon away since you have better leverage.
By allowing the area above the guard to be used for gripping also (circled in red, above), it allows the user to switch between using it like a sword (hands closer together), or using it like a polearm (hands further apart).
As you can see in the above 3 stances, they look highly similar at first glance. But upon closer observation, we can observe some differences in the front hand's position on the blade. This is verified with the version found in the Ssang Su Do chapter of Muye Dobo Tongji, which is also based on General Qi's Long Saber, and I had similar findings.
First, the Long Saber is being used as a Polearm, that's why the RIGHT HAND is on the blade. In regular swordsmanship, there are instances and techniques where you'd have one hand on the blade, but it's usually your left hand, so that you dominant right hand can continue to grip on the handle.
But in this case, you're placing your dominant right hand on the blade, which suggests that you're not trying to do some half-swording techniques, but rather you're using the Long Saber as a Polearm.
If I'm correct, then my guess is that the different hand positions are based on Chinese Spear techniques of 攔 (lan) "Sweep", which is turning your palm facing upwards, to deflect to the outer-side. When your right hand is forward, your outer-side is your right side. And of course 拏 (na) "Parry", which is turning your palm facing downwards to deflect to the inner-side.
This would then make sense for General Qi to dedicate a drawing for each unique technique.
4th Stance (Not In Video)
The single handed thrust (Green Dragon Bares Claws) is a very common technique in fighting with the Chinese Spear. It can give you a tremendous amount of reach in a split second, but you'll also be in trouble if the enemy blocks the thrust and you're left with only 1 hand holding onto the Spear.
The "Dead Deflect" stance is one historically documented technique to salvage such a situation, where you'll pull your Spear back and upwards, allowing you to defend your head while you regain your grip.
Does the above (extreme left) Long Saber stance resembles such a technique, if you consider that you're using it like a Polearm?
Ancient Chinese Martial Arts Manuals