I have a lot of experience with this exact problem. When I started training I used to just get bulldozed by bigger guys who wouldn't try to open my guard, but just pin me and sit in it until I opened it, and then try to work to pass. I have picked a few guys brains on the subject, and their answers have worked a lot for me. Here are my suggestions:
1.) Sit up on them. This is a piece of advice I have heard over and over and over from guys much better at jiu-jitsu. If you sit up and grab the head quickly, now the pressure is on them. Unfortunately, if he's grabbing your wrists and actively pinning you, you're not going to be able to do this without opening your guard and scooting your ass back shift the angle. It is a great piece of advice, but really only applies when the guy is sitting back.
2.) Bring your knees to your chest. It sounds like you've already worked this out, but it is very important to do it with a closed guard. Personally, I find it helpful, especially if the guy is leaning in a little bit to increase that pressure. It'll often totally kill his posture, especially against new guys, and allow you to work your guard up higher.
3.) Make sure your guard is high. Attacking him from his hips can be effective, but it is going to require you to open your guard way more often than attacking from when your thighs are in his ribcage and armpits. When your guard is higher, you don't need to open your guard dramatically to attack him. This was a piece of advice I got from a purple belt I was working with for a while, when he realized that I basically had no closed guard game. Having the guard high on his body is often much more threatening, and may force him to let go of your wrists to try to work your legs, and then you're on offense.
4.) Sometimes you just have to be patient. Getting relaxed from your back can be very difficult, but I think that it is important to remember that sometimes you are just going to need to learn to be comfortable in uncomfortable positions. One of those positions is going to be when a guy is applying direct pressure to your body and controlling your limbs. If you don't feel threatened from such a position (and if, incidentally, you are ahead on points in a match) you have the benefit of playing it cool for a while and letting him make the first move before you mount your counter-attack.
Hope that was at least somewhat helpful. I realize that those things can be challenging, since they're more theoretical than detail specific, but the details are going to depend a lot on your preferred attacks and counter-attacks from the closed guard.