"should" in the subjunctive mood

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Can we use “should” in the apodosis of an unreal conditional sentence?

In many English grammar books, they say that we can only use “would,” “could,” and sometimes “might” in the apodosis of an unreal conditional sentence (for example, “If I were you, I would do that.”), and even if we use “should,” it is usually used as the past tense of “shall” only in British English, which means that it doesn’t mean like “need to” or “ought to.”

So if we want to use “should” to mean like “need to” or “ought to” in the apodosis of an unreal conditional sentence, how do we do that?

For example, “If you could have gotten good results, I should (that means like “would need to“) give you a toy you want as a reward, but you couldn’t, so I shouldn’t do."

I know this sentence is kind of disgusting, but is the use of “should” here correct? Or must we use “would,” “could,” and sometimes “might” in the apodosis of an unreal conditional sentence to avoid using “should” when we want to mean like ”need to,” or “ought to” in the subjunctive mood?