I think in what you have written there are fundamental errors and/or misconceptions. We cannot tell whether this is because of what you understood from what you have been told or what you actually have been told, but that is that.
The key to control and breaking the posture in a way you can profit from in closed/half guard is not necessarily about hips - and certainly not the neck - but about wrist control.
Think about it: How are you supposed to yank down an opponent by grabbing his neck - working against the biggest and strongest muscle in all the body (back) - with your arm and a bit of weight (the upper body is not that heavy, really)?
So if you want to get somebody close, you will have to get hold of their means to keep distance - the arms. As long as the opponent is able to push with their hands from the hips into your abdomen, you cannot possibly break posture.
Hence, the first step is to control the part of the arms that you can move the easiest - because it is the farthest away from the big muscles in the torso: the wrists. Fighting for wrist control is fighting for control in this case. If you do not fight for the opponents' wrists, they will use their back and their weight to retain posture and eventually get one of your knees to the ground to escape. Having the wrists (and hence arms) out of the way, you will see that the rest is fairly easy.
Whether you achieve that by actively meeting the grip fight before your opponent gets hold of you or e.g. by turning your hip/shrimping so that you can move the grabbed hand from your abdomen to the side of your hip/torso is situational. There are many situations and possibilities. But the fundamental is to clear the way first.
One last point: Fighting for the wrists is fighting for the centerline. That's where arms and grips are dangerous - holds true for standup game as well.
The key to control in any control/mount position is not actively producing pressure by tension, but passively by relaxation and restriction of movement through strategic positioning of limbs.
To clarify: The most common mistake is full body tension. If you do this, your weight - which is the one resource you do not have to use energy for - is distributed away from the opponent's torso by your effort, i.e. you effectively use energy to lose control.
Your hip should always have (slight) contact to the mat. Your active pressure does not come from above, but from the side (hey, side control?!), i.e. you keep your toes on the mat and push sidewards into the ribs of your opponent with your torso fairly relaxed - that way your weight works where it is: On the opponent's ribs.
Also, your arms should not be overly tensed. They are locked, yes (and this means hands locked, elbows close and turned inwards - ideally under the opponent's shoulder, i.e. close to your belly button), but the shoulder-into-neck magic should come from your body/feet, i.e. "forwards" pressure of all your body into the opponent's, so that as soon as you shift your shoulder forwards, there automatically is pressure where it ought to be.
The bridging/shrimping escapes then are countered with a) turning of hips (so that the weight is on your attacked side and it is impossible to slip under your body) and b) following the shrimping direction by pressure from your feet/legs. If the opponent moves, you have to move as well. It does not make any sense to try to retain the exact position by use of force since it only leads to the expenditure of energy you so desperately need in the ground game. But this is active interplay and cannot be grasped by words/explanations so much as by experience/feeling.
Ground game in general
Your main goal is control, i.e. shaping the situation so that the opponent has (a lot) fewer options than you for moving. Lying flat on your back in the closed guard is obviously not a good position with that in mind, closed guard has to be a transitional state with a lot of movement.
High-level grappling consists in shaping the options of your opponent so that whatever option is taken, it leads to even fewer options and eventually to submission. The main component of this is gradually getting hold of more parts of the opponent's body or at least to a stronger grip on the ones you have, i.e. usually starting with wrists and ankles/knees, aiming for one shoulder plus neck (the magic triangles from where you can do most submissions, regardless whether with leg- or arm-control).
Controlling the hip, in particular, is very hard as it is the centre of mass, the place where the biggest muscles come together, and hence the place where the most momentum can be generated.