I think yes, yes, yes, and yes to those 4 factors. Any one in isolation probably wouldn't mean you'd experience any problems on the bike, but they're probably reinforcing each other in combination. Some back extension exercises would probably be helpful--stuff like supermans, and so on. I've really liked the exercises in Tom Danielson's Core Advantage book--they focus on building strength and stability in motion, rather than holding a static position.

Our muscles are more efficient in the middle of their range of motion, and less efficient at the extreme ends of our range of motion. When you're curved forward on a bike, the back muscles--especially if you're not very flexible in that area--are stretched out a little. Thus all the work that they do while you're riding is done at a position in which that work is a little more difficult for them to do.