Nope. Poked around a but more, thought .htaccess directives could do it but did not find a way. GoDaddy seems to configure to the lowest common denominator.
I'm learning that I agree with you. It really isn't much protection with this RC4 cipher suite enabled, but on the surface it looks secure. I did find a plugin called Really Simple SSL that has solved most of my security issues. They have a Pro version that will secure site cookies and a security scan feature. I did not find away to disable RC4 or Heartbeat (extension) issue. Please share fix if you find anything and I will do the same for you.
Really Simple SSL Free Version
success SSL is enabled on your site.
success Mixed content fixer was successfully detected on the front-end
success An SSL certificate was detected on your site.
success 301 redirect to https set: WordPress redirect
success HTTP Strict Transport Security was enabled
warning Secure cookie settings not enabled. To enable, get Premium