"Suppose, for example, the NSA was recording all HTTPS encrypted traffic to/from joeswebsite.com in January. Then, in February, they learned the private key for joeswebsite.com. Almost always, that lets them decrypt everything from January, February, March and beyond."
We should instead suppose that the NSA has had the private keys all the time (since it started recording encrypted communication), so every piece of communication that has been recorded can be decrypted even with Perfect Forward Secrecy. I.e. let's assume they got Google's private key immediately when it was last changed, then all communication with Google's servers is decryptable (correct me if I'm wrong).
The NSA doesn't have to brute-force private keys, they just use legal/strong-arm techniques to obtain them, so it doesn't take a lot of computing power and time.