When sharpening my western plane irons and chisels, after much experimentation, I've come to favor a very different approach to what I favor on knives.
Precise flatness for backs, edge straightness, and edge squareness are very important on woodworking tools. This can still be done freehand (I actually prefer freehanding to jigs with woodworking tools, as these actually change the bevel angle as you're removing material. You can actually maintain the angle better freehand.) with the aid of a small machinist's square, and practice.
Your first step is flattening, and polishing the entire usable back face of the blade. Since you have a lot of hardened steel that'll be in contact with the stone on a western chisel, this is very hard work and takes a ton of time, but you only need to do it fully once. You need to get these as precisely flat, and perfectly polished as possible.
Because of the slurry release, I've found I can never actually get chisel/plane iron backs perfectly flat on coarse synthetic water stones. They always end up a little, or a lot convexed depending upon the softness of the stone, and muddy ones can hide irregularities that will be unveiled on finer stones. Western woodworking tools are of a soft enough steel to not suffer damage from diamond plates, and the hardened steel wears out the plates less than soft cladding, so it's the best solution I've found. I personally start in the 220-400 grit range, and work my way up to 600-1200 grit on plates, then switch to hard synthetic water stones once they get fine enough not to disrupt the flatness too badly, though I'd keep going on even finer plates right up until pre-finishing/finishing stones if I could. Since there's so much hardened steel in contact with the stone, your grit jumps need to be a lot smaller than on knives. Doubling sometimes is a bit of a reach...
When you get to the finishing stage, I'd take it to an absolute minimum of an 8K synth, though even higher is better, and hard J-Nats are the best. You want the backs to get an absolute polish.
Then you'll be doing the edge bevels. You want these to be square, and with the right geometry for the application. I'm personally not a fan of micro-bevels, and prefer to either do either a finer single-angle bevel for pairing and delicate work, or a convex edge (Using a rolling stroke) for more durability on rougher cuts.
On the older planes and Stanley Sweethearts you mention, inevitably the backs and edges will be WAY out of joint (Settle in... It's going to be a very long haul to getting all of these in working order.). Due to the construction of Japanese chisels/planes, you don't have the hassle of back flattening, and the edge bevels tend to be ground a little better out of the box. Honestly, if you want to sharpen on water stones exclusively, ditch the western Chisels and go Japanese, but realize they're a little less durable and have a shorter lifespan in exchange for all their advantages (More wear resistant steel, namely.)... Western hardwoods tend to be rather abusive on tools, so I actually favor western planes and chisels, since these are the woods I work with, and I'm a masochist when it comes to sharpening projects. Mono-steel chisels and plane irons last longer in situations you know they'll get beat-up.
American/European tools tend to be like vintage French carbon kitchen knives... They're indestructable and long lived, and can feel wonderful in the hand, but they need touching up constantly during use. You'll want a 600-1200 diamond, 2-3k water stone, a pre-finisher (5-6K synth, or natural stone), and finisher (8-12k synth, or natural stone.) very close to hand. You can sometimes be taking apart your plane, and sharpening touching up every few minutes depending on the wood.
Japanese tools are like Japanese knives in the kitchen... More fragile, but you're sharpening less often, and your sharpening media don't need to/can't hog off as much metal. Because of the ura, though, they'll have a shorter life if you know you'll be fixing chips from hammering on them.
Japanese chisels get sharpened like single bevel knives... First you thin and shape the bevel (I use a mix of synthetic and natural stones only for this.), and then you flatten the ura on a fine (6-8K or finer) stone, before alternating strokes on ura and bevel.
My current western woodworking tool progression is:
Atoma 140
Dianova Coarse
Dianova Fine
DMT Dia-Sharp Xtra-Fine
Shapton Glass Stone 3K HR
Hard La Verte Coticule (Partial slurry progression.)
Bare Horse Butt Leather Strop
If I could do it all over again, I'd use a full DMT progression from Xtra-Xtra Coarse to Xtra-Xtra Fine, then switch over to a J-Nat progression (Probably starting at Aoto or Tsushima, then onto a Lv.4-5 finisher with nagura.). If I had to use synths, I'd do a full Shapton progression to 30K... I have the 10K Chosera/Pro, and honestly, this isn't even as fine as I'd like on woodworking tools, but it's workable.
My current Japanese woodworking tool progression is:
Shapton Pro 320
Naniwa Pro/Chosera 800
Hard La Verte Coticule (Full slurry progression)
Bare Horse Butt Leather Strop
If I could do it all over again, probably my only change would be if I was sharpening Shirogami rather than Aogami, in which case I'd use a full J-Nat progression past 320-500 grit Shaptons.
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You can sort of cobble together a progression on your existing stones, but honestly I'd get at least an Atoma 400/DMT 325/Dia-Sharp Coarse/Dia-Wood 300 to bridge the 140 to Naniwa 800 gap in replacement of your Naniwa 400. You'll also find yourself badly wanting in that 4-5k range to bridge the gap between 2 and 8 Naniwa, or Numata then Aiiwatani/Suita. I'd fill this gap if you can with a synth or natural, and maybe even think of a Lv.5 J-Nat or a really fine synth (12-16K) for finishing... Woodworking tools, like razors, almost never seem to get 'too fine'.
In the Naniwa range, the 800, 3K, 8K progression would work, but you can always go finer. Alternately, the 2K, 5K, 10K. If your Nakayama is Lv.4 or over, I'd finish them on this.
I can't say anything you have is 'ideal' for woodworking tools. Kitchen knives and woodworking tools/razors are utterly different progressions in terms of stones.
You could go something like coarse diamond plate, Naniwa 800, Naniwa 3K, Naniwa 8K, J-Nat Lv.4-5 finisher. Alternately, Dianova/DMT Dia-Sharp/Dia-Wood 300-325, then Dianova/DMT Dia-Sharp 600, then Numata, then Aoto, then Suita, then Lv.5 J-Nat. Either of those will be ideal progressions. Replace the diamonds with 400 and 800 Naniwa on your Japanese tools.
You'll also want a bare, ideally horse-butt, leather strop.
Hopefully this helps...
-Steampunk