Couple tricks:

I don’t have my flute in front of me, but I think you can hold the low c pinkies down on the g.

I agree g could have pinky left off as another option.

We have a trick as flute players to rub our pinky over our nose before doing that type of move. It puts just enough grease to help slide.

For the air, it has to aim down. Buy a pneumo pro and have them practice moving from second fan from bottom down to bottom.