As for the kind of grease, beyond the one recommended at the KSS, I have no idea. I work in a printshop, where I asked for the best type of grease and this is what I use - but for our purpose it doesn't matter:
The amount of grease should be minimum of the minimum, imagining a micronic layer of grease covering all moving parts. As for the instruments - there are no real instruments but METHOD. Sometimes you will use your smallest finger, and for intricate parts you may use a tooth wooden stick, but always almost invisible amounts.
The idea is not to try to paint all the gears with grease at a single strike, but leave a minimal amount at one or two spots per wheel, and then wind and fire, wind and fire, dozens of times G E N T L Y, not looking at TV but feeling the camera, feeling the winding. I strongly recommend to change in progressive and regressive order the shutter speeds, let's say after 10 firings at 1/1000, you change to 1/500 for another 10 windings and firing, etc.
For the sake of safety in not damaging both ends of each curtain, where they meet and engage, I propose to divide the greasing into two stages. Stage 1 with the back chasis open you will deal with the gears uncovered by the chasis. Stage 2, after you are done here, close the chasis and start greasing the upper gears around the winding knob. In both stages you will discovering more and more moving parts to grease. Everything that moves should be greased.
When you are done and your camera fully re-assembled, you will not be really done. You will have to carry the camera with you everywhere, even if it is only to work, or in case you are a student at home just to the bathroom. Shoot some 1 to infinity shots per day. This way the grease will further expand and all components of the camera will find their inner harmony.
During that month you will see by yourself that the camera is changing and things not so soft today will became further soft, like if the camera was a living organism.
But let me clear the other extreme: the idea is not to hit the camera. It is like letting the camera walk a lot, by natural pace, on rubberized shoes.
Hope I have answered most of your issues, at least to the best of my knowledge.
Cheers,
Ruben