Should as Future Perfect Modal

We say:

"The installation should have finished by now"

and we can say:

"The installation will have finished by tomorrow"

But what about this:

"The installation should have finished by tomorrow"

"I should have finished the homework by the end of the week"

They might be uncommon, but even so, that may not make them ungrammatical. It is all about whether being used or not.

What other modals can be used with future perfect other than "will"?

---

Edit:

I would like to post an authentic example I have acquired from COCA as an evidence to the correctness of this grammatical construction.

Glim's shoulders droop a bit. He looks over at me, " Nothing. You? " # " Nothing, " I say, shaking my head. " Sorry, Serba. These aren't responsible. Nor do they suggest any meaning or use. " # " I never really expected they would. I only hoped.

Perhaps we'll learn more from the experiments next week. You should have started your tests by then as well. " And perhaps the disrupters will no longer be necessary, she sends. I shrug. Hope seems far away, given Madrin's position. She is, after all, a telepist; her opinion carries the weight of the Interplanetary Department of Justice behind it.

Date: 1996

Publication information: June 96, Vol. 90 Issue 6, p129, 32p
Title: Communion.
Author: Gross, Gordon
Source: Fantasy & Science Fiction

Another quote is this:

When you have seen the student regularly, you may need to take steps to break dependency. It may be helpful to bring the issue into the open and agree that this session ought to be the last. It is always possible for the student to make another appointment if they really feel they need it.

The next interview may be more productive if you make it clear what work or thinking the student should have completed by then.

Managing Teaching and Learning in Further and Higher Education
Kate Ashcroft, Lorraine Foreman-Peck
Psychology Press, 1994

Answer

Using this as a reference, these sound OK, with the exception of "have to" but only because repeating "have" twice like that sounds a bit jarring.

I ought to have finished the homework by the end of the week.

I have to have finished the homework by the end of the week.

I shall have finished the homework by the end of the week.

I have heard this before, it sounds a bit awkward but makes sense.

I had better (typically "I'd better") have finished the homework by the end of the week.

I have also heard this before, it sounds quite awkward but still makes a bit of sense.

I have got to (typically "I've got to") have finished the homework by the end of the week.

This ...

I must have finished the homework by the end of the week.

I must not have finished the homework by the end of the week.

sounds like you are just discovering you have or have not done the homework, rather than using "must" to communicate a requirement or obligation.

---

However, usually all these sentences are arranged like this, which sounds much more natural to me.

I ought to have the homework finished by the end of the week

And all the modals "work", including the ones not mentioned above, if you keep the sentence like that:

I can(n't)/could(n't)/must(n't)/might (not)/may (not) have the homework finished by the end of the week.

(Even though "I must not have the homework finished by the end of the week" - meaning I am required to not have my homework finished by the end of the week - is a peculiar situation to be in - that would be the right way to say it.)