To be honest, I never really focused on any of the JLPT tests, but do you take in a lot of (comprehensible) input? Like watching gaming streams in Japanese, AHK Easy news podcasts, watching movies? It is pretty active and difficult to do, but over time it gets easier.
I found that my "speaking ability" totally skyrocketed after hearing certain grammar structures so many times from native speakers in actual conversations. For some situations, I came to realize that I don't even know why I say certain things-- just that it feels right to word it that way. And I haven't really had strange looks from native speakers when it happens like that. The only way you can build up those kinds of instincts is to hear it repeatedly.
The comprehensible input also helps you after awhile when it comes to speaking, since you'd be prepared to keep up with a conversation and can just parrot variations of what you've heard more easily.
Granted, this is all under the pretense that you can already understand basic sentences and such.