What kind of filter can remove zeolite dust from ethanol?
Since this never got a proper answer I thought I'd come back with a follow-up.
Essentially the root cause was low quality sieves (I had just picked the cheapest I could find on the internet). There are probably other things that work but all of the following captured the dust when used alone:

Whatman #6 filters do a decent job. I have #597 too but I don't recall if they worked here. (Whatman filter grade chart).
A bed of sodium bentonite over a #597, which  I was using to filter other stuff, also incidentally captured the sieve dust.
I never actually tried celite; but it was recommended in the comments so that could be a solution, too.

And the following also helped with the issue:

Simply letting the solutions sit for a day then pouring off the top left a significant portion of the dust settled at the bottom. I'd do this anyways before running it through a filter, to lighten the filter load.
More importantly, they were just cheap sieves. The second time I used them after baking them there was significantly less dust, and by the third time the issue was basically solved.

The next time I get cheap sieves I think I might wash them in the solvent first just to get the initial dust load out, recharge them, and then use them for their intended purpose. Although I suspect that if I balance the time, cost, and energy of doing this with the extra cost of better sieves, it's probably a good idea just to pay for the better sieves.
Pretty obvious in retrospect but maybe a fellow non-chemist will find it useful some day.