don't do supermans....that's just extending from the lumbar spine...bad mojo.
stretch your hip flexors...look up some dead bug exercises and double leg lowering...which are kind of like your wall exercise...they should be easy to find on the net.
overhead work is great...just make sure to squeeze your butt and brace your abs while you're doing it. planks are great too. make sure you squeeze butt and brace abs while doing them. one thing you should keep in mind all day long is not moving your lumbar spine
learn to move from the hips and not the low back.
the beginning of my journal has a decent amount of rehab/corrective exercise type stuff you could look at.
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And when you seek forgiveness
You will see there is no god
And for all eternity
You will cry my name