This might not work with a prolapse, but I personally use my hands to push and avoid using my internal muscles to bear down as much as I would like to-instead I focus on relaxing them. I do this by pushing in towards the sacrum and down below my belly button on both sides with all four fingers of both hands in sync, in a kind of massaging action (massaging down, then down again-not up, like the kind of action that the colon would normally do). I get more traction if I put the backs of my wrists against my thighs when I do this. It helps to get the pouch emptied, particularly of gas. If I feel like I'm having too much downward energy/motion, like a dull pain in the lower abdomen, I massage back up after I'm done emptying. I wouldn't do any of this if it causes pain, though. You know your body, so you'd know if you experienced discomfort that was signaling you not to do it.
Yeah, I seem to respond much better to non-invasive, non-radical stuff, like the yoga techniques that have been around quite some time. Those bandhas are pretty old health care-they came way before most of the yoga we commonly see people using for exercise.