I disagree slightly
But since we're staying nice and civil, there's no great reason to mind yet
Whilst I agree there are several different ways of answering a maths problem, I argue that the ways of answering an essay question are far greater. Whilst there are a few general "formulas" running around "SEXY", "SEE", "the hamburger" etc etc, I've found that most people who use this format as their "formula" rarely get anything higher than high band five, maybe low band six. Good for some, but if you're aiming for higher (which I guess we all should)...
I remember discussing this last year with someone. To a certain extent you can look at an essay with a formula in mind, and do particularly well. In fact, if your essay structure needs improvement, following one of the guides ("SEE" etc) is probably an excellent place to start, to familiarise yourself with basic essay format - what needs to be put in there, and how.
But when you start with the more hard-core integration and answering of the question, the "formulas" often just don't cut it. Although, they and guidelines can be useful (I think your list up above is more of a guideline) but I guess what I'm trying to say is that a really good essay, a really good one - just sort of flows. You don't have time to think "oh, I need to write my statement now... then I need a quote" because you're working on a slightly higher level. On a lot of high band 6 essays I've looked at, it's clear that they haven't followed any "formula at all" (I was able to check with most of them - they tend to use metaphors like "A good essay is like a good spine, all connected but with the little bits sticking out to support it" to describe essays, rather than statement/example/think/evidence/answer the question!").
Onto language now - yes, you can strike high in the sophistication stakes by using the sophisticated language, however you can almost make yourself look like a complete idiot when you use them in the wrong context. Markers aren't stupid. They can tell when you've used a thesaurus, even *I* can tell when a student has used a thesaurus.
My theory is that we write the way we think. Anything we don't understand and are able to use in context up here *taps head* isn't going to be understood and used in correct context down there *taps paper*. It's good to want to be fancy, but only if you know what you're talking about. Don't just insert the words into your essays - put them into your vocabulary as well.