Use of "should have" in conditional sentences

The NOAD reports the following notes about would and should:

The traditional rule is that should is used with first person pronouns (I and we), as in "I said I should be late," and would is used with second and third persons (you, he, she, it, they), as in "you didn't say you would be late." In practice, however, would is normally used instead of should in reported speech and conditional clauses: "I said I would be late"; "if we had known, we would have invited her."

The sentence uses what the NOAD calls the traditional rule, where would is normally used nowadays.

Should can indeed be used to express the conditional mood, although the New Oxford American Dictionary marks it as “formal”:

should
3. formal  expressing the conditional mood

• (in the first person) indicating the consequence of an imagined event: if I were to obey my first impulse, I should spend my days writing letters.
• referring to a possible event or situation: if you should change your mind, I'll be at the hotel; should anyone arrive late, admission is likely to be refused.