One problem is the third premise: if you believe in an open future, you may also believe that ‘p will be true at t’ has no truth-value – although p will acquire a truth value at t. Setting this aside, I think the use the first-person pronoun ‘I’ gives rise to some trouble. (As a quick way to see this, just try to run the argument with e.g. ‘Frank is dead’ instead of ‘I am dead’.)
If a sentence contains an indexical like ‘I’ (or ‘now’ or ‘here’), we can’t ever say that the sentence is true or false simpliciter: we can only say that it is true (or false) at a given context c. In turn, a context (according to the common definition) is an ordered n-tuple, containing at least an agent, a time, and a possible world. (It might contain other stuff like a location, an epistemic standard, etc.) At a given context c, e.g. ‘I am home now’ then expresses that the agent of c is home at the time of c.
Importantly, the ‘agent’ of a given context c needn’t be saying anything at the time of c. In fact, it’s not even clear that the agent of c has to exist at the time of c in the world of c. (Kaplan thought they must, but people have found good reasons to disagree.) Because of this, a sentence like ‘I say nothing’ or ‘I am not talking now’ will turn out true at some contexts – viz. at all contexts c where the agent of c is silent (at the time of c). And that’s a good thing: otherwise the sentences would be logical falsehoods according to the logic of indexicals!
With this in mind, we can return to your ‘I am dead now’. While there are no true utterances of this sentence, there arguably are contexts at which the sentence is true – viz. all those contexts c where the agent of c is dead (at the time of c).
In sum, there are ‘future contexts’ at which ‘I am dead now’ is true. Thus, even if we accept the third premise, the conclusion still doesn’t follow.
