If I absolutely couldn't go underground with SWA, then catenary wire the other side of the gate might be worth a ponder.
If you stick with conduit following the route shown on the photos, I'm not following why you would choose to put them in that exact position or why they are in fact needed. Sorry if I'm missing something.
So it will follow the same route down the house but where the bend is I’m looking to replace it with a Wiska or adaptable box then go straight across. As the arch is going and a new gate in its place. There will be another box on the right, on top of the wall. Then across into the garage.