Sorry haven't read the full thread, but I have incessantly dry hands and here's my tips.
if your hands are sore / inflamed it could be eczema and some strong steroids cream / ointment might help calm them down in the first instance.
Carry hand cream with you, and any time you wash your hands during the day, make sure you dry them thoroughly, then put cream on straight after you've washed them.
Type of cream is totally individual as to what works, so I'd say rather than go for a specific brand, try a few or try different types. I like using colloidal stuff as it soothes my skin.
For very dry and cracked skin - use foot cream or heel balm!
You're doing the right things using rubber gloves, avoiding contact with water etc and also gloves outside to avoid the cold air making them sore.
Drink plenty water.
Eat plenty "good" fats as these are good for skin (nuts, avocado, nut butter, seeds, etc)
Dry skin can also be due to dietary intake, possible intolerances or sensitivities. For example my eczema is worse if I eat a lot of sugar or processed food, especially cheese or wine - it flares up. and improves if I eat well - so whole foods, home cooked, meat, fruit, veg.
You could try supplements for skin too, Google it and find something that supports healthy skin, try it!
Hope you find something that works, it's awful having sore hands. I often have to take my rings off, avoid hand washing too much and use all the creams until mine calm down.