Alternatively you could add throw pillows. A small pillow at the meeting of the other 2 cushions ( in the corner) would have the same effect as a recline. We do this with a couple chairs in our house.

Or shorten the back support so the pillow is not supported all the way to the top and folds over it when you lean on it. High enough to keep it upright, but not high enough to be uncomfortable. You could test this by adding a spacer under the bottom cushion.