In American English, "should" and "might," in this context, are not idiomatic. A native speaker of American English would not use either one in the sentence unless they were pretending to be (1) pretentious or (2) British, or unless they are part of a fixed phrase or construction that has preserved this archaic idiom: "I should think not!", for example.
As a native American English speaker, I would use "would" or "could." They do have slightly different meanings, but in context, the differences are unlikely to be important.
In the sentence:
He knew that no one would ever discover his secret
the speaker is talking about whether a thing will happen. In:
He knew that no one could ever discover his secret
the speaker is talking about whether a thing is possible. In practice, they are more or less interchangeable. If you want to understand the difference, consider this sentence.
The smartest man in the world knew that no one would, because no one could, ever solve his devious puzzle.
Here, the speaker makes this distinction expressly: it will not happen, because it is not possible.
In my understanding, "might" is a British, and possibly archaic, variant with roughly the same meaning as "could," and "should" is a British, and possibly archaic, variant with roughly the same meaning as "would."
If I am going to eat somebody, it might as well be you.
This is acceptable. The prohibition against futurive will is a prohibition against that word in that sense, not the future reference. In any case, be going to in this context is present-focused: it expresses present intention or expectation of a future event.
It might as well be you literally means “You would serve as well as (or better than) another as object of my eating.” In actual use, however, there is no modality or tentativeness here. Might as well in this context announces a decision to accept an invitation or opportunity:
A: Wanna go grab a beer?
B: Might as well.
(Actually, in my dialect it would be “Mought's well. Can’t dance, and it’s too wet to plow.”)
The sentence may be paraphrased “Given my intention of eating somebody, I have decided to eat you.”
If I was going to eat somebody, it ... ?
This is trickier. Was here is acceptable colloquially as a variant of formal were. In some contexts it might express uncertainty or hypotheticality, but in the context of my intention it almost has to express counterfactuality: “I do not at present intend to eat somebody, but if I did ... ”
Consequently, it might as well be you cannot follow this. Grammatically it would be acceptable, but semantically the firm intention it expresses does not suit a counterfactual situation. And since its past-irrealis form (might) is already completely ‘modalized’, it cannot be modalized any further. To the best of my knowledge, even dialects which accept modal stacking will not permit this:
∗ ... it would might as well be you.
So you have to find an alternative expression. The closest I can get to a counterfactual version of the original is something like this:
If I was gonna eat somebody it’d definitely be you.
Best Answer
Need (like dare) is sometimes called a "semimodal" - it can pattern in some constructions like a modal, but can also be used as a full verb.
When it is modal, then adverbs usually follow it, as they do other modals:
When it is a full verb (followed by a to-infinitive) adverbs usually precede it:
These placements are not compulsory (the other order is sometimes possible) but they are the most common pattern.
Note, by the way, that in my (British) English, modal need is not particularly formal: They need never find out is perfectly possible in casual conversation.