Repairs to Large Stone Wall

I have a new neighbour - not the other half of my semi-detached house but the other side.  Their house has a door onto the pavement, whereas my house is set back 15 metres, with the result that there is a wall  between my front garden and their back garden. They have done a phenomenal amount of work on their place in a very short space of time (mostly based on the right principles). One of the things they have done was to remove the huge amount of ivy on this 16" thick limestone wall which, sadly, has revealed that the wall is not in as good a condition as I thought.

The wall is of a mixed construction being partly coursed random rubble and partly roughly

squared - see photo (the bin is just there to give an idea of scale). Where it was clear of ivy (left of picture) there are mostly blocks with good pointing, which is why I thought the whole thing was in good condition; however, much of the rest is coursed random rubble. The whole is capped by 3" limestone slabs, 16" wide and about 30" long; these seem to have been set with a small slope for drainage. Now that the ivy is largely cleared (the darker area where the ladder is), it is apparent that the coursed random rubble is in pretty poor condition with loose or missing mortar, ivy penetrating the wall and loose stones in the first couple of feet down from the top.

The wall starts off pretty vertical (where it leaves the neighbours' house, out of the left side of the above picture) but moving away from the house it has a bow which means that the natural taper has become vertical on their side and a quite marked slope on mine. The top looks awful (left photo) but it's not possible to say what the original slope of the coping was; it has certainly increased a lot in places, but I don't have an clinometer so I can't measure it.

The trouble is that the wall is pretty big. My side is about 8 ft high, and their garden is probably about 3 ft lower than mine (as my garden slopes up and theirs is level throughout), so they have an 11ft wall towering over their patio. A major rebuild is definitely needed; legally I think it's their wall, but it's my ivy. Both houses are listed and in a conservation area. A like-for-like repair does not need LBC but, as it's so high, I'll find someone more experienced to do it for me, rather than do it myself as next year's project. I wouldn't want the responsibility if it fell over later.

I've had a builder look at it and his view is that the bow means that the top has moved over a foot out of true, which is a lot, and so it looks as though the neighbours and I will have a discussion about this with a view to rebuilding the top few feet sometime next spring!