How do you keep crushed stone inlay from crumbling off a bowl rim?

The epoxy crowd is right on this one. I've done a bunch of crushed stone inlay, turquoise and lapis mostly, and thin CA over packed chips always gives me that same flaking you're describing. The super glue wicks down between the chips but it doesn't coat them evenly, so you get weak spots right at the edges where the sanding bites in and pops chips loose. What works better is mixing the crushed stone with epoxy to a thick peanut butter consistency, troweling it into the channel, and packing it down hard with a bit of dowel or a putty knife. You want it slightly overfilled so it cures proud of the surface, then sand back level. Use slow-cure epoxy, not the five minute stuff, because the five minute gets hot and can kick before you've got it packed in properly. A toothpick dragged through the fill also helps chase out air pockets.

Your channel dimensions are probly fine, honestly. An eighth deep is a bit shallow for a quarter wide though, so if you get a chance to deepen it a little before committing the bowl, do it. More depth means more epoxy locking the stone in mechanically, not just sticking to the walls.

For sanding, start with somethig coarser than you'd think, like 80, on a flat block so you're leveling the fill and not just polishing the high spots. The wet sanding was smart for keeping dust down but yeah, lapis dust gets everywhere. On walnut the blue-gray in the open grain is hard to avoid entirely. What helped me was sealing the bare wood around the channel first with a coat of shellac before filling, then sanding, so the dust has nothing porous to settle into. Wipes off the shellac surface easy. As for cloudiness under oil, oil finishes will darken lapis and can make it look duller since the stone is porous. If you want it to stay bright, tape off or shellac the band after leveling, then finish the rest of the bowl. Or just plan on the stone darkening a shade and let it look intentional.

I did crushed malachite on a maple platter a couple years back and the thing that saved my sanity was scraping instead of sanding for the leveling part. A card scraper takes the fill down flat without tearing chips out like 80 grit does, then you only need light sanding after. Also, once it's level I wipe a little thin CA over just the stone band and let it cure. That seals the stone so oil can't soak in and dull it, and it fills any micro scratches so the lapis polishes up nicer too. Worked way better than taping everything off, at least for me.

I'd push back on sealing the bare wood with shellac before you fill. If any shellac gets down into the channel or onto the walls, the epoxy isn't bonding to wood anymore, it's bonding to a finish, and that's exactly the kind of weak edge layer that popped your test piece apart in the first place. Masking the rim with tape while you fill, then pulling it before the epoxy skins over, keeps the dust problem mostly solved without putting a release film where you need adhesion. The walnut around the channel is going to take some dust no matter what, but a soft brush and compressed air after leveling gets most of it.

This thread is making me rethink my own project, I was going to try crushed glass on a small hollow form and had the same worry about the walls flexing while pressing the fill in. Did anyone find a way to pack it without putting pressure on the rim itself? I was picturing supporting the inside with a hand or a form but I don't know if that's a real technique or just something I made up. Also second question, if I wanted to crush my own stone instead of buying it, is there a grit size people aim for, or does chunky versus fine change how it sets up in the epoxy?

On the flexing rim question, I just leave the piece on the lathe when I fill. Spin it slow by hand, pack the fill with a short length of dowel and light taps with a small mallet, and the chuck takes all the pressure instead of the walls. Did that on a 10 inch walnut vase last spring and the rim never budged.

One other thing about the stone itself, run your crush through a kitchen sieve before mixing. The big chunks are what bridge across a shallow channel and leave voids under them, and that's ussually where the edges chip first, not the glue.