If you have lower-back aches and pains, you need to work on your lower-back muscles. Abs are naturally stronger than the backs and you need to bring the back muscles into balance:
The issue on the up-hills is that you're
pulling on the bars. Don't do that. Rest your hands on top of the bars and relax and curl your fingers into a loose fist with the fingernails resting on top of the bars. If you're wobbling all over the place due to an uneven pedal-stroke, work on your spinning form, don't compensate for it by yanking on the bars. You end up trying to oppose your leg-muscles with your back-muscles; guess who wins?
When I started, I had very strong legs from 13-years of playing soccer. Problem was that my lower-back wasn't developed enough to balance the leg muscles. I ended up pulling my back so badly on a sprint that I was bed-ridden for 4-weeks. PT and chiropractor helped me get back on the bike after 5 more weeks of walking around with a walker like a little old lady. The chiropractor was actually very versed in sports injuries and physiology and helped me improve my form so that I didn't need to yank on the bars to compensate for wobbling form. Spin-up exercises on downhills up to 200rpms really helped me stay smooth at lower speeds. And back exercises like shown above built up the back muscles. I got up to where I can do 20 reps with a 25-lb weight behind my neck. I never ever had back problems again in the next 10-years of racing.
As for the roll-the-hips-forward keep-the-back-flat form, here's what it looks like:

Notice in the 1st picture that the side-stripe of the jersey is straight and parallel to the ground. The bend is at the hips and butt, not in the lower-back. One way to get into that position is to imagine rolling forward on your saddle trying to put your belly-button on the top-tube. Then you need to slide back on the saddle to keep the weight on the back.
Another way to imagine that position is to stand up on the pedals like in pic#2. Then arch your back the opposite way to put your belly-button down. Then set your butt back down on the saddle. You should feel the jewels being pushed aside by the nose of the saddle (same as when you roll your hips forward).