Might this be wrong?

Here's what I'm thinking about right now. Andy Egan has a paper ("Epistemic Modals, Relativism, and Assertion" - Phil Studies 2007) in which he presents a simple argument for the thesis that sentences with epistemic modals express propositions that are true/false relative to a judge. The argument rests on the intuition that when person X hears person Y utter a sentence of the form

(1) Might φ

and when X knows that ¬φ, it is appropriate for X to say any of the following:

(2) a. What Y said was false
b. That was false
c. No, it cannot be that φ

However, consider someone else (Z) that does not know that ¬φ (or equivalently, for all Z knows, φ). It seems appropriate for Z to respond to Y's utterance as follows:

(3) a. What Y said was true
b. That was true
c. Yes, might φ

Given that X and Z can appropriately make these replies to Y and ceteris paribus any defeaters (whatever those might be), it seems that this lends itself to a quick argument for relativism about epistemic modals (X accurately reported that the proposition Y asserted was false and Z accurately reported that the very same proposition is true - taken at face value, this suggests that the proposition Y asserted is true and false relative to whoever is assessing it).

What I'm thinking about is Kai von Fintel and Anthony Gillies' paper (ms) "'Might' Made Right". In that paper, they propose a case just like above, but argue that X may respond to Y as follows,

(4) That's right. Might φ

If that is right, then this takes some of the wind out of the relativist's sails, since the relativist wants to say that what is relevant to the truth of epistemic modal claims is what is known by the assessor of the sentence (in this case, X). But in this case what X knows rules out φ so it is not true (relative to X) that might(φ). How would the relativist account for the acceptability of X's response (4)?

But is this response really acceptable for X? Though I am currently in California, a friend of mine, M, doesn't know this and is trying to find me. It is compatible with what she knows that I am in Connecticut, so she says,

(5) Justin might be in Connecticut

I am evaluating her utterance, knowing that I am in fact in California. Would it be appropriate for me to say,

(6) That's right, I might be in Connecticut (?)

(Imagine we are playing some weird phone version of Marco Polo if it helps to put us in conversation with each other). (6) seems to be a very weird and misleading response for me to make, though putting stress on the might alleviates some of the badness. While I don't have strong intuitions one way or the other, here is one reason to think that (6) is bad:

(7) ??I might be in Connecticut, but I know that I'm not
(8) ??I might be in Connecticut, but I am not

Any reasonable account of 'might' must account for why these are bad (either contradictory or unassertable due to some pragmatic rule governing assertion). Now, given the set up of the case, we should all agree that the second conjuncts in (7) and (8) are both assertable for me (I know where I currently am). But then given that they are both assertable by themselves and their conjunction with (6) is not, it seems we have good reason to think that (6) is not assertable for me. I can't think of any examples of two propositions that are both assertable yet their conjunction unassertable (except for Gricean reasons involving "but" - if that bothers you, then change the "but" in (7) and (8) to "and"; the result seems even worse!).