That stiffness could be achilles related, which means it needs to be treated gently, while calf elasticity becomes paramount importance, and it is not easy to do both at the same time.
I find that mental tension builds up around the region you describe, the back of the heel and around the sides of the heel, and the mental adjustments to pain-stress you posted about recently should be directed to relaxation of that region.
Also, a simple and non-harmful technique: with foot relaxed take heel cord in two fingers behind ankle and gently wiggle it to and fro (it may not seem like it will wiggle when you look at it but it will easily do so if you try). Work your way up the calf until it connects with the calf muscles, and massage up the muscles.
This will take the tension out of the cord, but maybe only for a minute or so. Still, that's a break in the stress.