I wouldn't go for down either for active use. Especially under a shell mitt they can get wet quite quick when active. If in camp then great of course.
I get very cold hands when stopping as well.
My layers, when active:
-Thin liner glove or thin leather climbing glove (I like the Rab M4's because of their incredible dexterity).
-OR PL 400. These are really warm double layer (100+300) fleece.
-OR GTX shell.
Lost the shells in the Mont Blanc somewhere (not on the mountain, in the refugio or on the way down). Replaced them with Black Diamond Soloist Lobsters.
The BD Soloist Lobsters also come in mitts, but I like the lobster design because it is a bit easier to handle an ice axe or trekking poles. I can always stick my index finger in the remaining finger section if I get too cold. They come with their own Primaloft mid layer, so I alternate those with the OR PL 400 gloves while I dry the other out if necessary.
For emergencies / longer breaks:
More as an extra / security layer for deep winter (-10/-20ËšC) I bought Rab Endurance Down Mitts. These are stupid warm and you can stuff the down more or less to the hands or cuffs (like you would with a sleeping bag).
I bring some chemical heat patches just in case.