Learn English – Is “how much ever” correct here

That's a "trick" question because it is not about what follows "best", but simply about "should you use 'in' or 'on'?".

The double-trick is that in some case, you could (with a slight variation of context) use 'for'!

I'll do my best for the TOEFL preparation so I'll get higher score on the exam.

Anyway, if we stick to the initial choice 'in' or 'on', the final trick is in some case, both could be used, like the two first examples ("on" maybe being more commonly used in the US)

I find (personal rule)

• "in" standing for "during" or "within" (or other similar meanings)
• "on" standing for "about" or "referenced by" (or other similar meanings)

Meaning I don't find your examples "wrong".

I'd have expected your first option to be far less common than the other two, but a couple of Google Ngrams show that this view is probably unwarranted. Only 'at least' seems to be commonly used, though the other two are not unknown. I'm surprised; I'm quite familiar with 'at the very least' as a pragmatic evaluator.

At least (as a pragmatic marker – mitigating), as you say, has a different meaning, unwanted here.

I'd avoid at the least as sounding unnatural, though there's no grammatical reason why at the very least should be correct and at the least not so.

You could go with at the very least, which sounds a little over the top to me. I'd rephrase to 'It causes at least one problem: ...; it might also cause others.' This usage of 'at least' is as a quantifier rather than a pragmatic marker.