Less money, less time -> synthetics. More money, more time, more fun -> naturals.
I think JBroida's point is that to save time he'd use synthetics up to the fineness of edge he'd like, which is around what your natural finisher is - your Takashima - and then switch to the natural to draw the benefits from using that. Can't blame him as I imagine he sharpens rather a lot of knives each day. You could easily use a coarser natural between your 800 and Takashima, though.
May i enter? I'm not sure that the real matter is the progression or the stone type or the grit of the whetstone. Every steel ( stainless or high-carbon) reacts differently on same whetstone ( whether synthetic or natural), so why not to ask what knife has to be sharp? Yeh - one can achieve the required edge on many abrasives - but if to go that far (diff. Jnats etc) , why not to take into consideration the type of the steel used in the knife? The softer steel can be sharpened even on the opposite side of the tea pot , doesn't it?
57-59 R is not the same sharpening as 62-64R. The progression is different, the invested time etc. Stainless knife ( not the PM knives) are easier to resharpen as high-carbons. I have a good range of synthetics - and some high-quality 8000 grit synthetics - sometimes they are faster on some knives, but they never give me that sence and that feeling of the edge that the good Jnats does. I agree - this is about the time to invest , if we talk about a jump from 800 or some other coarse stone to a good Jnat. Earlier or later you will get your cutting edge in the desired condition, this is the question of time. One medium grit stone in-between would speed up the process.