Burn the aft tank first. Leave it on auto.
Your instability is created because the CoG is too far aft. Burning the front tank worsens this. If you burn either tank, the resulting loss of weight makes the plane feel a lot better. However, the stability at that point is dictated by which tank you burn. Leave it on auto, except burn your AUX before your DT (if you take full fuel).
EDIT: Take a centerline 500kg bomb, 100% fuel. Climb over target to 10k. Burn off all your front tank. Dive on target, release bomb, pull out about 2k. You will rip your wings off. Do the same but burn off the REAR tank instead of the front, and you don't rip your wings off. It's because the CoG is behind the wings, and pulling up stresses the wings more because the pivot point has shifted.