Should we worry that the risk of omnicide is increased by the growth of movements like EA and longtermism that draw attention to the extent and prevalence of suffering and the desirability of its reduction?
One way of ending suffering would be to eliminate all life. If we convince more and more people of the problem of suffering, and the necessity to do something about it, do we also inadvertently increase the likelihood that some people will conclude that to end suffering we must end the world? With technological advances, it is possible that a very small number of actors would need to be convinced that this is a good idea for it to become a real risk over time.
Your concern about doomsday projects is very welcome in this age of high existential risks. Suffering in particular plays a central role in that game. Religious fanatics, for instance, are waiting for the cessation of suffering through some kind of apocalypse. Many negative utilitarians or antinatalists, on another side, would like us to organize the end of the world in the coming years, a prospect that can only lead to absurd results. For the short term, doomsday end suffering projects can plan to eliminate life (or at least human life, because bacteria and other small creatures would be extremely hard to eliminate on this planet), but I doubt that they would want to have consideration for "the conditions for the evolution of life throughout the universe", be it only because they are completely unable to do anything about that, or because they are anyway not rational at all in their endeavor. So, there is a race between us and the doomsday mongers: I think that bringing a solution to suffering is our only chance to win in time.