Cassette cogs in Shimano IGHs & spacers
 

Feel free to correct if needed.

Hubs: Nexus SG-8R36 & Alfine SG-S501

IGH cogs (Shimano, Sturmey Archer) are 3mm thick at the base.These cogs are held in place by the snap ring.

To get desired ratio, plan on using 8-and 9-speed cassette cogs after grinding away 6 splines and shaping the remaining 3.
Only when Shimano & Sturmey Archer cogs with required teeth are unavailable.

8-speed cogs are 1.85mm thick.
9-speed cogs are 1.78mm thick.

How thick should spacers be for the snap ring to hold the cog in place?
Obviously, it is 1.15mm and 1.22mm but spacers of that thickness are unavailable.

Do the spacers need splines?
What did you use?
What do you recommend?

Have you tried one from a shimano coaster brake hub? Should be the same 3 spline pattern. I have 22's and 24's in my junk so I know they can be found.
I did a random search on google and came up with These they are interchangeable with coaster brake cogs from shimano and sturmey

Seems like a lot of work. Remember to not exceed the maximum rated number of teeth on the hub sprocket (or whatever sprocket combination gives the maximum input torque).
The spacers wouldn't need splines because it doesn't matter if they rotate.

Schweinhund Got 23t and 24t (1/8", easy to find 1/8” chain) .
sweeks What is max rated number of teeth on hub sprocket?

As I understand this issue, it's not so much the maximum size of the hub sprocket, but the minimum ratio of the front sprocket to the hub sprocket. In this LINK, there is a reference to a minimum of 2.1.
I could not find an "official" specification for this minimum, but HERE a poster claims it is 1.43:1. If the front sprocket is too small for a given rear sprocket, the hub may be exposed to too much torque and could be damaged.

In this Tech Doc the largest recommended hub sprocket is 23 teeth. This may have more to do with which sizes are compatible with the cassette joint than input ratio.
If the 2.1 minimum ratio is correct, the smallest chainring that should be used with a 23-tooth hub sprocket is 48 teeth. If you go by the 1.43 number, the chainring that matches the 23-tooth sprocket is 33 teeth.

On the other hand, Sheldon Brown's SITE seems to suggest that this minimum ratio is not a factor for hub reliability: Usually, manufacturers rate hubs in terms of the acceptable chainwheel/sprocket ratio, but this rating really amounts only to "we will make it so hard to pedal that you will get off and walk." Pushing a lower gear up the same hill actually stresses the hub less.

So, depending on your reasons for wanting to adapt a cassette sprocket to the geared hub, you may want to consider this ratio as well as whether the hub sprocket will interfere with the cassette joint.
I hope this makes sense.

3 spline IGH cogs in 13-24T flat and dished are so readily available that there's no reason to consider using anything else.

You can get them in 3/32 as well, and 1/8 chain will run on that.
Here's a 22 in 3/32 https://ultimatesportstrinidad.com/p...-22t-y33060100

I hadn't thought about the dish... using a flat sprocket could mess up the chainline. As I said, seems like a lot of work... and what would be the benefits?

sweeks good point about interference with cassette joint. Sheldon Brown expresses it in his style. I spin rather than mash and don't get out of the saddle while climbing. If I can't spin my way up, I just walk.
Alfine 8 & chainglider requires flat cogs.

dedhed in some sizes, supply is limited, esp the less expensive Sturmey Archer cogs

Schweinhund true

I'm pretty sure the chainglider works with the standard shimano hub sprockets, or there would be a market for flat sprockets with the standard 3-point interface. To my best* knowledge, these don't exist.
(*Aye, there's the rub!)

KMC lists 27T and 30T sprockets in the ubiquitous three-tab pattern.

https://cimg2.ibsrv.net/gimg/bikefor...c0d52182a3.png

Sturmey-Archer's three-tab sprocket offerings in the classic interface diameter:

https://cimg1.ibsrv.net/gimg/bikefor...1076508733.png

Of course chainglider works with dished cogs in general, but not with Alfine 8 hubs. Sneaky guys - this incompatibility is listed in the installation instructions.

Just cannot find 27t and 30t cogs with 3 tabs. May I trouble you for a link, KMC & one seller?

https://www.kmcchain.com/en/product/sprockets-s-n
27t & 30t have 6 tabs and recall reading that grinding off 3 excess tabs doesn't help since the tabs are at different positions compared to cogs for Nexus & Alfine 8.

Thanks for improving my "best" knowledge! :D

Revisiting this topic.

Found a guy with CNC setup. He is willing to try to convert 9-spline cogs to 3-spline cogs. But has no idea how to specify the splines in IGH cogs. I don't either.

Can the shape of the splines in IGH cogs be characterized or specified in geometric terms? Perhaps an equation?

The steel in those cogs is so hard it is not easily modified. Just try taking a file to it to see what I mean. Roger