I'm your weight and for these sails I would surely pick the 71. I sailed it a few times with 5.3 and it works very well, even if it's onshore and a bit underpowered.
As you may know, the 71 and 76 have a bit different shape. The 76 is a v into concave design while the 71 is the classic EVO concave into v. But in the big scheme of things this is of lesser importance and I would say the two boards rides rather similarly. When I change between them there is no adjusting of technique or such things. So you can safely let size decide and go for the 71 which is an awesome all round size for people our weight. The 76 has a big range too, but is more of a light wind board for me.