the white haze stayed all the way through 180 grit.
180 paper is actually fairly coarse in the grand scheme of things. It is a perfectly fine final sanding grit for wood in most cases (and sometimes you can get away with stopping below this) but for other materials it's quite common to sand far beyond 180-220 grit because the scratches left by paper of this grade are still large enough to be easily seen with the naked eye — if you continued to sand through to 600 grit much of the haze on the epoxy fills would go away as the surface scratches became microscopically fine. And sanding finer and finer, to grits beyond 1200, the epoxy surface would become become incrementally clearer and more glossy.
This isn't to suggest you should sand the slab to anything like this level however, because as soon as finish goes on the hazy/clouded appearance will instantly vanish. You can preview this effect by just getting a finger wet with salive and wiping it over one of the fills.
Note for future readers: depending on the final finish you'll be using and the method of application it may be necessary to sand a little finer than 180-220, and it might take more than one coat for this non-clouded appearance to be permanent, although with some finishes (e.g. undiluted varnish or lacquer) just a single coat is usually enough. In simple terms the thinner the finish (e.g. penetrating finishes like oils) the more you'll benefit from sanding more finely, 400 grit is probably a good minimum to aim for here, and the more coats will be needed for epoxy fills to maintain their clear surface once the finish has dried.
The following are unrelated to your main query but I wanted to touch on them since you included them in the details of the Question.
I followed online guides that suggested mixing a small quantity of sanding dust (I got mine from 120 grit paper)
Couple of things about this.
First about quantity, you can add as much or as little as you like but generally you add more than a small amount of powder to use as filler. Structurally you can get away with adding so much the mixture becomes a stiff paste (generally likened to that of peanut butter.... and it can look exactly like peanut butter in colour too). Starting with a fluid epoxy and if using wood dust alone as the filler material the minimum amount that gives a dense (not somewhat transluscent) colour will generally yield a consistency akin to softened butter or maybe mayonnaise1.
In terms of the dust itself, generally it's advised to use dust generated by finer paper than 120. 220/240 grit or so is a fairly common choice and somewhere in that region should be considered sort of a minimum2. Finer dusts give the most uniform 'unspeckly' result as well as the greatest strength, but for simple surface fills outright strength matters little and if you're happy with how the fills look with coarser filler material then don't worry about it3.
My next step after sanding to 220 was going to be to hit it with several coats of a water-based polyurethane, then sand/buff that to a perfect gloss.
I think it's worth mentioning that this is not the ideal finish type to use to finish off in that way. Waterbased finishes in general can be a little on the soft side (even ones containing polyurethane) and additionally can get gummy when they heat up during buffing operations, but the specific one you pick makes a huge difference here.
I would advise doing a preliminary finish check before committing to the expensive slab to test out your proposed rubbing out and polishing process using the waterbased poly. Ideally you'd use an offcut of the slab if you have one but use another wood if you have no spare cherry.
1 The general consitency stages are often given as syrup (unthickened epoxy), then through ketchup, mayonnaise and peanut butter as filler proportion is increased, see more here on the West System site, Modifying West System Epoxy with Fillers and Additives. Also worth reading, the formulas and tips for MAS Epoxies Wood Flour on the SMS Distributors site.
2 Where wood dust is used professionally as filler it is often bought in as wood flour, and as you might guess from the name this is very fine.
3 Many people have experimented with coarser particles for filler, up to and including sawing waste with little flakes and chips of wood that give a distinct speckled or flaky appearance, showing that individual taste is really all that matter here.