I have made my points regarding bolting the gates, and stand by them, but to practical issues.
I am not a civil engineer, my grandson is, and his expertise is in the use of concrete.
I would have thought, at least in the case of Rampgill entrance, it should be possible to peel back some of the ground either side of the arching and pour in concrete.to reinforce the whole structure, and possibly force re-bar into some of gaps between the arching into the wet concrete ,hence spreading the load and re-inforcing the gate plates.