Assuming you believe in the heat death of the universe, that is, its entropy will, in finite time, reach a maximum (as a function of time). Let's consider a chain of events $\mathcal C_1$ starting now with the Universe in its current state, leading up to that heat death and leaving the universe with a final entropy $S(\mathcal C_1)$. Mathematically speaking, $S$ is a function which maps a chain of events to the subconsequent final entropy of the universe, regardless of when it is reached. Would a different chain of events $\mathcal C_2$ (also starting now) lead to a different value of $S$, that is $S(\mathcal C_1) \neq S(\mathcal C_2)$ ? Otherwise formulated, does the value of that final entropy depend on what goes on in the meantime ? Can I alter it by creating entropy ? Or on the contrary, is the entropy of the Universe at its heat death computable given enough information on its current state ?
No, because by definition that maximum entropy state already corresponds to you having your maximum entropy. At the time of the heat death the temperature of everything would be the same, and no heat transfer or work could take place.
If you want to increase your entropy in this very moment, you have to take in heat from somewhere else. And there would come a time when you are forced to give back that heat, because everything around you is becoming cold.