Learn English – There would be/will be/might be

SHORT ANSWER:
Might cannot be substituted for would because they express different degrees of ‘modal’ certainty.

LONG ANSWER:

1. May/might and will/would, like other modal verbs, have a variety of meanings, classified by linguists as deontic (having to do with obligation), epistemic (having to do with inference) and dynamic (having to do with action and intention).

   But throughout these shifts in meaning, may/might and will/would exhibit a consistent contrast in modal certainty. Here are some present-tense examples.

   • May always signifies a possible but not certain event.

     DEONTIC: You may go to the lecture. = I permit you to go the lecture (but I do not require that you do so).
     EPISTEMIC: That may be Kevin at the door. = It is possible that that is Kevin at the door (but it may be someone else).
     DYNAMIC: I may go to London tomorrow. = I am considering going to London tomorrow (but I may decide not to.

   • Will, on the other hand, always signifies necessity.

     DEONTIC: You will go to the lecture. = I require you to go to the lecture, no ifs ands or buts.
     EPISTEMIC: That will be Kevin at the door. = It is Kevin at the door, no question about it.
     DYNAMIC: I will go to London tomorrow. = I have a firm intention of going to London tomorrow.

   When modal verbs are cast in the past tense, the range of readings becomes more complex, because the past-tense forms may signify actual past tense, or present ‘tentativity’, or present counterfactuality. Combining the past-tense form with a perfect construction adds yet another layer of complexity: the perfect construction may be either a true modal perfect or a ‘sham’ perfect in which the have + Pa·Ppl is secondary tense marker which resolves the ambiguous time reference of a past-form modal. But the contrast between possibility and necessity is maintained throughout these shifts.

2. In your original examples the contexts make it clear that the two would have beens employ epistemic wills cast as indicatives. The first has a true modal perfect, while the second employs the perfect as a secondary tense marker.

   At home I locked myself in. Jason, my lawyer and Lyn sent texts simultaneously at the point the announcement was made. Lyn would have been sending texts consecutively for 15 minutes. ... That is, I was certain that Lyn had been sending those texts.

   A: We saw a police helicopter overhead yesterday morning.
   B: Really? They would have been looking for those bank robbers. ... That is, I am certain that they were looking for the bank robbers.

   In either case, replacing would with might would change the meaning by downgrading the sense of certainty from necessity to possibility.

   At home I locked myself in. Jason, my lawyer and Lyn sent texts simultaneously at the point the announcement was made. Lyn might have been sending texts consecutively for 15 minutes. ... That is, I thought it possible that Lyn had been sending those texts.

   A: We saw a police helicopter overhead yesterday morning.
   B: Really? They might have been looking for those bank robbers. ... That is, I think it possible that they were looking for the bank robbers.

Lost opportunities

The meanings of these are indistinguishable, except for a subtlety that I'll explain later:

We may have been able to save the victims.

We might have been able to save the victims.

The words "would" and "could" suggest both the past tense and the consequence of some imagined hypothesis, with either or both meanings being activated when suitable to the context. To use "would" here, you need to establish an imagined hypothesis. Then "would" indicates the consequence:

If only we had the antidote yesterday! We would have been able to save the victims.

It's possible to say "could have been able to", but "could" is the past tense of "can", so it already indicates ability. So, "could have been able to save the victims" is awkward. However, you could say:

If only we had the antidote yesterday! We could have saved the victims.

"Would have" and "could have" imply that the opportunity is now lost.

"May have", "might have", and "could have" don't require context to set up an imaginary hypothesis, but they do suggest that you have such a hypothesis in mind:

"We might have been able to save the victims."

"How?"

"The most recent antidote has been sitting in the refrigerator since yesterday."

"What? And no one tested it?"

An important difference

A very big difference between the may/might and would/could sentences is that the would/could sentences claim a high level of certainty about the hypothetical situation: the antidote is assumed to work. The may/might sentences lack that certainty. They suggest only that in the hypothetical situation (which might not even be stated yet), the antidote might have worked. "Would" corresponds to "will", and says that the antidote will work (in the imagined situation, which occurred yesterday). "Could" corresponds to "can", and suggests that the antidote can work (in the imagined situation, which occurred yesterday).

A subtle difference

"May have" mainly indicates uncertainty about what we could have done. "Might have" suggests both uncertainty and that the opportunity, if it even existed, is now lost.

This is English, so don't take that as a rule. Instead, memorize this well-known couplet (by John Greenleaf Whittier, 1856):

For of all sad words of tongue or pen,

The saddest are these: "It might have been!"

One more power of might

There's one more possibility with "might", which illustrates the flexibility of these words. "Might" can suggest that the victims actually were saved, or are actually in the process of being saved:

We might have been able to save the victims. I just read an article in a medical journal, which says that the antidote we tried yesterday was proven to work on mice in a recent experiment.

In other words, the antidote we tried yesterday might be working, right now. Since the uncertainty of the word "might" applies to our ability to save the victims, if we had that ability yesterday, then our efforts yesterday were successful, or are on the way to succeeding. Currently, we don't know (that's the uncertainty of "might"). Obviously, your listener will hear this meaning only if the victims are still alive.

You can also do this with "may have" and "could have", but those don't make the pun in the title of this section. Since "may have" has the least connotation of lost opportunity, it provides the clearest way to express optimistic uncertainty about the effects of yesterday's action: "We may have saved the victims."