My guess would be that the reason you can't currently stop the height loss, is that the head is not the causation of what's really happening as you take the club back.
If you think about it the head can't dip on it's own account, so the focus needs to be on what is really causing the height loss during the motion.
Obviously haven't swing the swing but generally in my experience there are usually 2 main ways this can happen.
First & less common, is during the backswing the lower body, hips & gluts both sway a ways to the right with a 'sit down' move, not very often this happens.
Second & much more common is from the get go of the move away the legs are active, in particular the left leg, left knee.
So on the takeaway instead of the legs initially staying a ways solid to resist the chest & shoulder turn plus arm swing into the backswing.
Unfortunately there is an active movement of the left knee, both backwards towards the right knee but also outwards towards the ball/target line, it's a big left knee 'bend' (collapse), so the whole leftside lowers some. (causing the head to move downwards as a result)
This 'bend' & height loss also causes a couple other things we don't want to happen, it means going back that the weight then stays largely on the left leg. (instead of turning into the inside of the right foot, & right knee staying flexed as the hip 'turns' into the right hip socket)
This also means that the shoulder & chest can't 'turn' properly.
With this left knee collapse & the weight mainly staying left, the upper body can only really tilt.
As the left shoulder is moving downwards & lowering (not turning back) & the right shoulder is tilting upwards,
So a proper shoulder turn never really happens & it feels like it can never either complete properly to the top & the upper body never really gets behind the ball, if anything it usually with this has the spine also leaning wrongly towards target, either level with the ball or even in front of the ball, so the upper body never gets behind the ball properly.
All this usually means going back the right leg straightens a ways too. So to try to get the club far enough back because the shoulders haven't turned to around 90º because with this action it's impossible, the arms often too then get lifted up away from the body.
So top of back swing the weight is proportioned the wrong ways round, still mainly on the leftside. (instead of on the inside of the right foot)
So on the downswing the weight then can only go the wrong way onto the right leg, which is also a ways too straight.
So the weight is going a ways right while the upper body arms & club are trying to go against it the other ways to get to the ball.
The right leg being straight means there a feeling of not being able to get down to the ball properly, with the weight on the right still, the hands/wrist flick some to get thins/tops or high weaker flight, or the club gets dumped in the ground so fats, depending how this wrist/hand flick is timed.
So the focus shouldn't be on the head, as that really isn't the cause.
The focus, so cure is having a good address position/posture & from that a better backswing upper body chest & shoulder turn/coil over a more solid base with the legs (no more 'Elvis' knees) so the weight moves with the turn, moves in the same direction the club is traveling.
The legs, left knee, & hips move in the backswing because the upperbody turn makes them move (usually around when the arm/hands pass the right thigh)
You don't want the left knee moving straight from the get go when the shoulder/chest & arms start the takeaway.
Here's a good way of understanding how the upper body has to 'turn' over a solid base, so no left knee collapse (just a freaky co-incidence that this Pro's name is .... Knee!!)
I'll put another vid up following this one as well. With a drill that can be done inside to get a better correct upper body shoulder/chest turn. With the club shafts (or shaft & alignment rod) giving a marker, that one is one top of the other the turn is a sound one, collapse the left knee & tilt & it's impossible to do this drill properly.
[video=youtube_share;pK5jGCjAdoI]