Adding STMMaskableGraphic didn't make any difference. I'm using the Universal shader. I tried Ultra with and without ZWrite and there's no difference. The only possible thing I can think of is the info panel attached to each hex, which has it's own canvas - but I have those that completely disabled (parent object is inactive).
All I do with the map hexes is instantiate them from prefab (into a parent with lower sibling index than the object with the STM), and then set their sibling indexes within that parent. I'm not doing anything else that would affect rendering; so this is indeed very mysterious.
EDIT: I can confirm it's not the info panels - I deleted all of them in play mode and it made no difference.
EDIT 2: One other thing of note: If I stretch a single map hex and all its children so that it spans the "underside" of the quads, it doesn't cause this issue. It's only when there's a bunch of them active that this issue occurs. If I disable ~2/3 of them, then the quads show up. So it sort of seems like it's the number of images/objects that cause the issue. There's 221 hexes in total, each with 9 Images (plus 24 on the info panel, but that's disabled for this test).
EDIT 3: This actually has nothing to do with the hexes rendering on top of the quads. I did another test where I took a single hex that's far away from the quads and duplicated (at the same position) it a bunch of times. Once I hit 80 hexes, the quads disappear. Delete one and they show up again. There's no layouts involved here.