If it were me, I'd just keep writing, keep them piling up, then sub the back log when the mags open, and that way you're not behind.

I don't really want to write genre fiction because I am still pretty new at general fiction.
That's interesting. I write contemporary fiction (non-spec), and a variety of spec fic. I think you can learn from writing any kind of fiction, and I go to a weekly group with a 'literary' teacher, but the tools she gives us can definitely help with any kind of writing. We all find our own style anyway. I write spec fic because its always been my first love, and hopefully you write general fiction because that is your first love. But yes, the submissions market for that is probably smaller. But if you don't write what you love, it would be hard to produce work that others love (and publish), whatever the market size.