Safe Elliptic curves of prime order according to "safecurves"
Are there any 'safe' and well-established elliptic curves of prime order?


Depends on what you mean by 'safe'.  If you use Dan Bernstein's definition of "safe curve", no; the curves they list as safe are Edwards curve, which always have a point of order 2 (and hence can't be of prime order).

As for proposed curves that are of prime order, there's the NIST curves that you know about, there's the Brainpool curves, and there are the Weierstrass flavor of the NUMS curves.  Whether they are 'well-established' is questionable; they each certainly have their proponents.

Also, it's not clear that you really need a prime order curve. The multiplicative group $Z^*_p$ you're using isn't of prime order either, you manage to work in a prime order subgroup.  The elliptic curves we use for cryptography have large prime order subgroups (to make the discrete log program hard), perhaps you can use the same trick to use, say, Curve25519.