I love these types of questions. It's thinking about jiu-jitsu conceptually, something that Nic Gregroriades covers in his book, The Black Belt Blueprint. I don't have it with me, but one way he put it was that if you are locking his hips, then all he has is his shoulders and arms. You still have the advantage of having your own shoulder arms and hips legs to control him. Of course, your own shoulder is engaged at his hips, so you have to release them to put them in a 2 vs 1 play (your shoulder/hips vs his shoulders - as you are past his hips).
I don't mind staying down there, if they insist. Ever since I found the truck entries from there, I have been even more comfortable there (there being low, reverse kesa or twister side control). Mount is very easy when they are worried about you wrapping up their legs. And, after I have been looking at Zog's Russian Cowboy series, if your school allows you to attack leglocks, that's another excellent option.
If you want to go to standard side control or kesa (judo side), then what I do is deflect their push either high or low. It locks their arms, occupies them against my torso, so that I can "switch" my hips first to face him, locking his own torso, then it's a "hand-fight" to get my arms around the head and arm. The key for me here is to NOT engage in that "win-chun" hand fight without having my hip weight on his chest, facing his head. If I try fighting his arms without enough control, then it becomes a scramble, and I lose the position, ending up in half-guard or even full.
Hope this makes sense. I recommend Nic's book because of it's conceptual approach. It's excellent for those seeking "the larger picture" as opposed to specific techniques.