To which "constants" is he referrin? Is he suggesting not using the NIST curves, which were themselves selected to avoid a different class of curve attack? Ok, then don't use those curves.
For end users, this is rather difficult. I maintain a Jetty web server, which is based on Java. The SSL/TLS implementation relies on the cipher suites provided by the JVM. I can restrict Jetty to using ECC as preferred cipher suites but not choose the curves. I assume this is also the case for many other web servers out there.
On the other hand it is easy to avoid ECC altogether in this scenario.
