I'd mix the two ideas... Get a thin liner pair to wear under the ones where the finger pops off... Best of both worlds.
No taking off outer pair, and fingertips still somewhat protected...
Edit - also worth noting that a good way to get heat to your fingers is to physically force warm blood out to them. This can be achieved by doing "arm circles", you know, the typical warmup exercise everyone had to do before P.E.... Doing them with relaxed, limp arms you'l feel the blood being pushed to your hands via centrifugal force... A bonus side effect is that it will warm up the rest of you slightly too.
And as an added note - when looking to keep extremities warm, think about the route your blood takes... All too often you see people layer up 2-3 pairs of socks in their thick rugged boots, and then act shocked when their feet are still frozen, when they have nothing more than a pair of jeans on their legs. This is effectively like running some exposed pipe down to your shed and then wondering why the radiator down there doesn't get very warm.