I've seen very few cervical lips in my practice--and only one that seemed to be a problem...but it wasn't. The 'problem' was that the baby was just stuck way up high, somewhere on momma's pelvis. We waited it out, after trying pushing for a bit (not long and not hard, because if pushing is going to help, it'll help without that much effort or time), and trying various positions/movements. When baby popped out from behind whatever it was, she came down in 2 pushes, no time to even mould her head...very suddenly.
Otherwise, with the few lips I've seen, I will generally encourage mom to push IF she feels like it--and see if that helps at all--some push right past it. If she doesn't feel like pushing, then we work more on keeping her strong--rested, hydrated, fed, supported (as/if needed), so that she will be able to go on, and figure it out or wait it out. I've never coached a mom to push for hours. When all is ready, second stage just wont' take that long. If it's taking that long, then something somewhere along the line is not ready! By the way, baby's can get born just fine, even w/out pushing 'urge'--if contrax are happening, then uterus will still push baby out. I can see how a mom might push for a long time under her own internal guidance...can't see how I would be 'helping' to coach her to do so in absense of that internal guidance. Almost every story I've ever heard of these hours of pushing (like, more than about 2, tho I most often see 2nd stages from 5min to 1hr), is a story where somewhere along the line, mom and mw each/both decided that it couldn't be done without interference and 'guidance'--one or both stopped trusting the process and started trusting the mw more (and the midwife's 'methods'/interventions). Decided that it was time to make it happen, instead of figuring out how to allow it to happen...and trusting that it would happen. That kind of pushing is so hard on moms, and can be hard on babies, too...far easier on both (if not exactly easy) to relax, wait, trust while staying fed, hydrated, etc.
Sometimes, I've seen that a lip does mean some kind of different presentation--head is not quite turned right or is not yet moulded enough, hand is up, something out of the ordinary or something (like sufficient moulding) that needs more time. And in these cases, it seems to help to get pressure OFF the cervix--laying down on side, hands and knees, or even knee chest, to take gravity's pull away from the equation. What I think is that when the head is 'being slammed against the cervix' as one pp put it, that makes it HARDER to open, not easier. Reducing gravity can reduce the slamming, and allow the cervix to completely relax. Along with the whole pelvis/back.
Maybe one day I will be at a birth where it seems right to push a lip out of the way. Haven't been to that birth yet. Either mom pushes past it without much ado, in accordance with her urge to push--or we wait until that is possible (or it disappears). And this waiting has not yet been a big deal to anyone...maybe it is more hours of labor, but a woman who is confident, fed, hydrated, rested where possible, and supported in any way she needs, will not get worn out from labor. And if she completely, really truly totally relaxes, this will happen sooner rather than later--head will mould or turn to right place, pelvis/tissues will adjust to that hand being up, whatever.
The mama in the forest, I think, would follow what her body was telling her...can't picture her messing with her cervix, tho I spose that's not out of the question.