I know exactly what you mean about grand canyon-sized gaps! I've had
fairly good luck with inserting leftover pieces of veneer (sanded
thinner if necessary, with a touch of glue or putty) into the gaps,
then sanding the surface carefully. You can orient the veneer
different ways as necessary to come close to matching grain patterns.
It's easier to work with if you use a bigger piece of veneer (leave
some sticking out while the glue dries) and then trim it with a razor
knife and hand sand. What kind of wood is it? If you can't get
veneer, maybe a thickish hand plane shaving from scrap would work. I
think glue-and-sawdust would work well too - could you scratch or stain
this filler to more closely match the grain on the staves? Practice on
scrap, of course - I could see myself messing something up by trying to
stain a 1/100" scratch in some filler that wouldn't really be visible
anyway...
Good luck, and let us know what works,
Andy