You described the differences pretty well.
In Destiny 1, shaders were normal items - they were not consumable. There was only one shader slot, and it applied to all your armor (weapons were not affected (related, most exotic weapons had one or two ornaments that worked similar to shaders, but were consumable)). You could change the shader at will, and the shader would not be destroyed. Later on in Destiny 1's development they added a shader kiosk where you could get a new copy of any shader you have ever found which would allow you to effectively use the same shader across all your characters.
In Destiny 2, shaders are now applied per item and can be applied to weapons, sparrows, ships, and ghosts in addition to armor. Shaders are also consumable - once you've applied a shader, you can't use it again. If you replace it with a different shader, the first shader is gone. When a shader drops, you typically get a few copies of it (I've gotten 3 at once, not sure if that is guaranteed).
The main issue some members of the community have with the new system is that in addition to being consumable (which means you tend to think about applying a shader, since you can't use it again), is that you can buy them with real money via the Eververse store. The conspiracy theory is that shaders were made consumable so that Bungie would make more money on microtransactions.
I haven't tried doing it with only 4 but with my experience doing it normal I don't believe it's possible. I've tried doing it multiple times after one person has fallen off and keep going with only 5 and it will end up stopping and you can't continue.
There are multiple videos showing how it's possible to skip parts or to do it solo, by using swords and supers to jump the gaps between reactors, but these will only get you to the last area with nothing happening. You have to get to the last plate on each section and have the "reactor temperature rises" message appear for each to actually progress and have the enemies spawn at the final area.
Best Answer
You are in luck my friend! With Season of the Worthy, they have brought back the Omega Mechanos set through the Eververse store. To find it, it's in the Archive Tab for 1500 silver.