As far as I know, the 11T cogs will only work in first position, and requires the notch on the end of the Shimano freehubs.
Perhaps they could be modified to work with extra thin spacers.
Chainline would be an issue. But there are a couple of different freehub widths. For Shimano hubs, the 7-speed freehubs are the narrowest that are commonly available that accept hyperglide sprockets & lockrings.
A few brands have "single speed" freehubs that are closer to 5 or 6 speed width, that could possibly be used.
I have some Capreo freehub bodies that are also narrow, and could potentially be modified to accept an 11T sprocket. But, the Capreo freehubs attach slightly different than other Shimano freehubs, so you'd be needing to replace the hub too.
That's what I was thinking.
It looks like there is a 11T Odyssey Driver
https://www.ebay.com/itm/Odyssey-Dri...D/332942620630
https://www.ebay.com/itm/Odyssey-11t...D/283375341289
In many senses, the BMX Driver's look a lot like the road sealed bearing freehubs (not Shimano), and it is quite possible that one could be substituted with a bit of tinkering.
Odd, the pawls look backwards in that Driver from Down Under. Perhaps they do things backwards down there.
