I suspect that if the lid isn't fastened down, the cows will find a way to move it - they just can't help poking about. That shaft near Elton that swallowed a cow a few years back had a cover on, though it may have just been timber or wriggly tin - but it was all long gone (and the cow long dead) by the time we got there.
It would seem to make sense to put any bolts well away from the edges - maybe a couple of clamping bars are better? So the lid is unfastened, but registers in the hole so it won't slip sideways. If one end of each bar was hinged there would only be one bolt on each to fasten? If they were done with expansion sleeves the bolts could then be screwed downwards into the sleeve rather than them protruding upwards. Granted the holes would have to be kept very clean and cavers mustn't lose the bolts!