You've asked two separate questions, and it is better to ask just one at a time; but I will attempt to answer both.
First, that use of should is odd for most people. There is an old-fashioned pattern of using shall instead of will, and should instead of would when the subject is first person ('I' or 'we'). Some people still use these most of the time; some people rarely use them at all.
Often it depends on the context; so for myself, I would always ask a question with Shall I? not Will I? (unless I am asking for a prediction). I often, but not always, say I shall ... rather than I will. (Of course in most conversation I say I'll, which neutralises the difference). But I rarely say I should for I would, except in the frozen phrase I should think... (Of course there is another meaning for I should = I ought to, and I use that readily).
My point here is that you example seems to be said by somebody who does use I should in that case. For such a speaker, the sentence is normal; but most people today would say I would there.
There is also the question of the tense: should or would there makes it hypothetical: I think most people would choose shall or will, to make it more definite. Even though the may in the last clause does strictly make it hypothetical, most people in that sort of situation would I think choose to be more positive, and state their intention with will or shall.
For the second question: the future perfect is not much used in conversation, unless it is needed for clarity. It would not be wrong to use it, but most people would say will be completed.