Actually, from the research I've been reading into, you can use the ash to help making charcoal. One formula uses plain newspaper, ash & whichever binder pressed into briquettes.
So, I spent more time researching, looking for recipes basically. And what I've learned is you can make charcoal from pretty much anything once it's been carbonized.
So, a basic recipe:
Get corn starch and dissolve in water, cook it til its a very thick paste (anyone ever make "slime" from corn starch? kids like to play with it. Same idea, just thicker.) Then add your char dust. Here's a somewhat large recipe:
"The usual formula for a briquette mix using starch is 100 kilograms of charcoal, 5 to 7 kilograms of starch, and 30 to 35 kilograms of water."
I'll let you all figure that ratio out in the smaller scale needed for your project at home
The mix should have a wet soil consistency once mixed completely.
Once you have your char paste mixed very well, you press it into shape. One suggested method was to use a tube (width can be whatever you have on hand or prefer) and a ramrod (dowel, or log if you're using a REALLY wide pipe) to press it very tight (some suggest using a mechanical press, such as a lever or turn-screw press; one cheap hack used a car jack as the lever on a wooden rig), then you can slide it out the end of the tube and slice it up while it's still damp. Let sun-dry for a few days and it's good to go.
This source has a lot of useful info:
You could make incense cones with the same mix, just add some drops of essential oils for fragrance.