To avoid the rain / material wear/stretch issues, a long time ago I started using a sort of webbing made out of nylon cord, 4 horizontal cords and 2 vertical, knotted together, to form a cylinder with a cord lock on top and a knot connecting all the horizontal cords that you use to hang it from.
Stick the bear bag in that upside down, cynch down on the cord lock to get rid of loose material, no stretch on the seams to leak since the bag itself holds no weight, no hole on the top to leak.
I used regular flat nylon cord on mine, nothing light, and it still only weighed 1/2 oz, if I remade it with zpacks or lawson dyneema core cord, it would only weigh a few grams. Using a bottom grossgrain strap seems like it would create stretch in the seam holes, that was my thinking anyway which is why I decided to avoid that method and just take all the stress off the bag.
This also lets you make a superlight food bag, even cuben, since the bag itself doesn't have to deal with any hanging stresses, all it has to do is hold the food in your backpack and inside the cord net.
I also like the ideas of a longer stuff sack and tying the cord around the neck to seal it, that's pretty clean too.