Too bad you can't wear wool. The only wool on my hands is a wool glove liner but you could substitute a synthetic liner (avoid cotton altogether). I have Ice Armor gloves and the liner/glove combo is good down to about 20 degrees F give or take a few degrees depending on wind, sun, moisture, etc. For really cold weather I've got a pair of Ice Armor extended cuff Extreme mittens that I bought in XXL which makes them large enough to go over the liners and IA gloves. Never had a finger get chilled with this combination down to -14 degrees F last winter. Believe it or not, there is still enough dexterity to shift and brake my flatbar touring bike, though you almost have to do it by sight as you can't feel much through all the layers. Luckily, the ground around here is almost flat, so I can start in a middle gear and pretty much stay there for winter riding as with heavy gear and wind chills I'm not going to be going that fast anyway.

Whatever you pick make sure there is a water/windproof outer layer, adequate insulation (Thinsulate brand synthetic insulation is pretty good if you get enough of it) and plenty of room to wiggle your fingers. Tight fitting gloves are a no-no in very cold weather and will actually make your fingers colder than lighter but looser gloves.