You need to still explain the origin of these instincts/why they tend towards empathy and if all they are are instincts, how do we know if they are right or wrong? This would be the is-ought fallacy because the way things are (morality based on instinct from your perspective) is not an indication that it is how it should be (that said instincts are right or wrong). So you still do not get real moral values based on your position.
If the instinct that was involved for instance is that we need to eliminate a certain type of people, say homosexuals who do not contribute to the survival of our species by propagating, would it then have been morally correct to eliminate those groups of people? If no, then the grounding for morality cannot be the empathic instinct. And if yes, your worldview is still subject to what you criticise the theistic worldview for. Morality would still be arbitrary because we cannot control how this mammalian empathetic instinct chooses to evolve can we?
Again, how can you empirically prove that the current level of suffering is excessive? You would need absolute knowledge of all the facts, past, present and future to accurately and objectively make that call. If you insist on making it based on limited facts, that is fine, but then it becomes a subjective call so why should anyone take your position seriously anymore than you take the theist's subjective "feelings that there must be a God somewhere" seriously?
Might I also add that excessive suffering does not equal unnecessary suffering. For instance from a Christian paradigm, the suffering of Jesus on the cross was massively excessive but necessary for the salvation of mankind. But even if I go with your logic, you still cannot prove objectively that suffering is excessive, you can only assume it.
Thanks for the response anyway