I fixed this on mine! Try the following, I really hope it works.
Put on two thick pairs of socks.
Force your feet into the front of the Converse but let the back flatten, so your heel is squashing it down rather than placed inside the back of the shoe. This helps start the softening. If it works better for you, force your heel into the shoe rather than flattening it, whatever's most comfortable is fine.
Wiggle your toes or walk around for a few minutes.
Next, with your feet still in them, blast a very hot hairdryer over the parts of the Converse that cause pain. Do this for exactly two minutes. If you flattened the heel, move your foot out of the way to blast the heel fabric. Leave your feet in them until completely cooled. This creates a moulding effect.
For me, that sufficiently softened/broke in the shoes properly. I only needed to do it once to both my pairs and they have been great ever since. They were a nightmare for many months before this. Hope it works for you!