Posted: 14/08/2016 at 22:46
It looks like it has struggled to get enough light so has grown away from the fence and what look like very tall overhanging trees. Unfortunately, there is nothing you can do that will encourage a mature tree to grow upright and hacking off large sections is something you are right to worried about for the reasons you mention. I would trim off some of the lower parts hanging down the slope now (summer pruning restricts growth) to make mowing easier and just enjoy the fact that you have a tree with 'personality'!
The old adage 'growth follows the knife' particularly applies to apple tree winter pruning so strong growth will occur where you prune it the hardest, which is the opposite of what most folk expect.