I second (or third) the doctor idea, if your hands are cold indoors. However, I do have a couple thoughts.
I myself find gloves ineffective below around 32 degrees, which is where I switch to mittens, so if you haven't tried mittens you haven't maxed-out the hand wear options.
As for which mittens, I discovered the following combination somewhat by accident.
A relative alerted me to Ice Armor 150-gram thinsulate mittens which seem to be intended for snowmobile use. They go up the wrist a bit and tighten around the hand. By themselves they are rather warm, but probably not good enough for you. However, I have made a "special modification." (By the way, they also have zippered slots on the backs for hand warmers, which I don't use.)
Some years ago, my brother who is handy with a sewing machine, made some mittens for my daughter to wear while standing around outside at high school ski meets. There was an inner mitten, and then a larger outer mitten made out of black fleece on the palm side and fake tiger fur on the back side (the school emblem was a tiger). They were long enough to go almost up to the elbow. That outer fake fur mitten was large enough to go over the inner mitten and therefore too large to wear by itself. However, what I tried to do is don that fake fur outer mitten by itself and then stuff the mittened hand inside the Ice Armor mitten. In other words, I have an inner liner for the Ice Armor mitten, made of fake fur, and enough fake fur to stuff inside the Ice Armor mitten and take up a lot of the excess space. For some reason, that fake fur liner inside the Ice Armor mitten is really warm, warm enough for me to be reasonably comfortable at below-zero temperatures. The liner mitten is long enough to go up the arm almost to the elbow, so it also covers up the jacket-mitten boundary and adds a layer of fabric on the arm.
So, if you have the time and a needle and thread, you could try making prototype mitten liners out of fake fur to see if you get similar results. It might not work for you, but it would not cost a lot of money to try it.