Brian Pickering's flute hold Jennifer Cluff on LH finger painIf your fingers are not very long, I think you are much better off with an offset G key, and it seems that inline G keys are not as popular as they used to be anyway, precisely because of hand and finger problems.
Sounds as if your flute is resting in a pretty good position - I find that the further the weight of the flute is to the SIDE, the more pain I get. I have very long fingers, and found that I was holding my LH very slanted to avoid curling my index finger so much. It actually worked better to hold the flute (as much as possible, anyway!) square on to the palm side of the base of my index finger joint rather than sitting it on the side of the joint.
What about your RH? The "modified Rockstro grip" which seems to be the bees knees at present tells you to bring the THUMB of your RH further to the back (your body side) of the flute to support it, rather than having it kind of hooked round the front. When I learned to do this, I found that immediately the flute was lighter on my LH finger joint - my RH thumb was holding the flute UP more than pressing it in and down.
Another tip - Scholl corn plasters stuck on the underside of your flute are often used to take some of the pressure of your index finger joint! I've even heard that a little patch of medium-grit sandpaper is effective, because it "holds" the flute better, and you don't have to throttle it in a tense, sweaty, death-grip.
And yes, shoulders and neck! You may have much less strength in those areas than you would expect! Belly-dancing shoulder shimmies are great for relieving stress in the shoulders, and swimming is great for upper body strength too. Failing that, how about "push-offs" (push-ups done against a wall, instead of off the floor)?
Best of luck!