Nicely put! I think the answer rather depends on what we mean by 'I', or again, what it is for me to be me (and you to be you), as well as what we mean by 'dead'. Here are some options:
1. If what I am is, as you imply, a psychological subject of experience, then I cease to exist at the point of death (assuming, with you, that dualism is false and there is no afterlife). Because I don't exist any longer, you are right that it doesn't make sense to say that I 'am' anything (even dead). As I don't exist, I no longer have any properties at all. It's this sense of 'I' and 'dead' that gives rise to your puzzle.
2. But perhaps what we mean by saying 'X is dead' is precisely that they have ceased to exist. 'Death', understood like this, isn't a condition someone can be in; it is non-existence. 'X is dead' means 'X does not exist any more'; to 'be dead' is not to be at all. So how can I 'be' dead? Well, one day it will be true for other people to say of me (and each of us) that I am dead. I, however, will never be able to say truly that I am dead!
3. But perhaps what I am is not a psychological subject of experience. Perhaps what I am is a kind of animal - a homo sapien. In that case, for me to be dead is for my body to die. Now, my body will continue to exist (for a while) after I am dead, so we can say that being dead is a condition of my body (me). Death is a change in the functioning state of a biological organism - from living to not living. So I can be dead. But I will only cease to exist when my body finally breaks up (by whatever means).