I have Godaddy’s Standard SSL 256-bit encryption on Linux. I get a worse grade than your site though when I test at https://www.ssllabs.com/ssltest/index.html ( you get an A and I get a C grade).
Looks like because my server uses RC4 and doesn’t have Forward Secrecy. Yours doesn’t support RC4 and has Forward Secrecy. This would just affect clients though. Depends on what Twitterbot demands perhaps. I’m not sure.
Do you have the Premium SSL plan? Don’t know if it matters since so far neither work.
Looks like All Really Simple SSL does is to redirect http to https, which can already be done in your htacess file.