Agree with core work in general. Specific recommendation: basket hangs.
http://www.danrobertstraining.com/15.html
Key is to avoid an arch in the lower back as you lower the knees down. Lower back should remain essentially flat--don't lower the knees too far, if you tend to arch as they drop.
The basic problem is that some hip flexors attach to the lower back. In distance running, the lower back tends to become too strong (and tight), relative to the abs, so the pelvis tilts forward rather than staying level, killing stride and efficiency.
A useful "drill": stand with your shoulders and butt against a wall, feet 8-12 inches from the wall, and knees slightly bent. (The first couple times you do this, you may find it useful to slide your hand between your lower back and the wall.) Now level (rotate) your pelvis so that your lower back is flat against the wall (or pressing against your hand). Hold that level-pelvis postition as you walk (and eventually jog/run) away from the wall.
Note that this is easier to do if your knees stay relaxed ("soft"); and that it's easier to keep your knees relaxed if you keep your elbows relaxed! At every speed, the elbow should open a bit as it swings back and close a bit as it swings in front.
This should not be a conscious opening/closing but just a consequence of relaxing the elbow and letting the weight of the forearm open and close it; this flexing is quite apparent at top speed (watch sprinters), but should still occur a tiny bit, even when you jog.
You can help make this feel more natural by concentrating on the backward, rather than forward, swing of the arms. To "drill" this you can think relax-back-relax-back for the elbows.
Kind of amazing that relaxing your elbows (and focusing on their backward swing) can help level your pelvis, but it really can! By the way: It also helps to reduce some of that cross-body armswing that your coach keeps harping on.