Agreeing with Lymond, probably you would gain more from military ambitions, in the sense of what can be provided by the forum.
Ideally you go Monarchy (which will also short-term alleviate happiness) --> Feudalism, in the meantime building Jumbos and Cats, which should be more than enough.
Not generally a fan of wasting production on Markets for happiness - Realistically, there should be enough whipping in the tank (especially once HR is active.)
Whilst I agree, ideally you'd trade Monarchy, I think it's the natural next step (or MC to lead to Machinery (Xbows can support elepult just fine.) - But if going for the very quick win, it's got to be Feudalism before MC/Machinery.)
I would be keen to ensure you take at least 1 more player out before Feudalism arrives (given that you can't trade monarchy currently, the AI is quite some time off from getting it.)