I agree with everything said above, but just some other suggestions for core.
I think walking with weights overhead is an awesome ab builder! Does not have to be heavy, just something. Also, maybe some overhead squats would help.
I also am a fan of front squats. Especially if you have the problem of going forward. If you go forward on a front squat, you lose the weight. I think actual ab exercises on do so much for stabilization. Heavy decline sit ups are really all I do.