First off, you shouldn't get inverted at take-off. That's insane and really scary (I used to do this all the time!
) You would need to say more about your plant for anyone to tell you if THAT was your problem. (Also, you can never go too fast.) Anyways, in order to invert, you need to swing up with a straight trail-leg and powerful drive-knee, AFTER creating potential energy in your pre-stretch/C-position during the follow through. If your landing shallow, it is more than likely that you aren't pushing the pole up past take-off. Do this mostly with your top hand, (bottom arm should be flexed out slightly,) and pretend you're trying to push the pole right over into the pit. A good drill to emphasize this is doing an approach and planting under a soft bungie around 8-9 feet above you. Try to hit it with the pole each time as you finish planting.
But if you're having trouble inverting, then most likely it's your swing up. Do drills to strengthen that, and make sure your take-off point is correct.