Green honing compound on a leather strop is around 5000x. Personally, I've gone the way of Yvsa and now sharpen everything "electrically" - giving most everything a convex edge.
One thing I've thought of trying is this:
Using a fine grit sandpaper held over the chakma.
The chakma is technically for burnishing, but I wonder if you could use it to sharpen as well - since it has a nice flat surface that would easily push through the recurve.
Here's how it would work:
Take a piece of fine grit paper (available at paint shops, metalworking shops, or knifemaking suppliers such as... *see below* ) and cut off a piece small enough to be able to wrap one-and-a-half times around your chakma. Use you thumb against the other flat side to hold the chakma flat against the edge of the knife. Then run it over the length of the edge - maintaining the edge angle you want.
Then, take a piece of leather loaded with rouge and do the same.
Correct me if I'm wrong, but if you were to start with 180 grit and work your way to 1500, and then a strop - you would have a nice edge.
I think I'll try this theory out this evening and get back to you about it.
The nice part of this idea is that you get the benefit of the chakma's flat surface and easy-to-manage size. (versus using a mousepad, stone or strop, etc.)
Dan
[edited to add sources]
K&G has 3M polishing papers that go all the way to 8000x
(1, 2, 3, 9, 15 and 30 Micron)
http://www.knifeandgun.com/catalog/abrasives_186628_products.htm
Texas Knifemaker's Supply has Wet/Dry sheets up to 2000
http://www.texasknife.com/store/s-pages/TKS_MainframeStore.htm
(click on "Abrasive Materials")