...I happen to have a [used] china bristle paint brush that's 1/2 the width of the above.
I rinsed the bristles with warm water, and ran a bit of ivory soap along the split-edged bristle-tips.
Then wrung out the bristles (similar to cleaning a paint brush in water, albeit allowing the moistened residue of the ivory soap to remain on the bristle tips).
Then ran the brush down my blinds, with the blinds closed.
I haven't tried applying fabric softener to the bristles, but I'm thinking that if anyone could get hold of wide paintbrushes at bargain price, then set aside one for the soap, and another for the fabric softener, maybe that would be the easiest (even if not so thorough??) method of cleaning blinds??