Your argument against nihilism is fundamentally "I feel the need to care about other people, and it doesn't help me to pretend I don't".
(I'll accept for the purpose of this conversation that the empty ethical system deserves to be called "nihilism". I would have guessed the word had a different meaning, but let's not quibble over definitions.)
That's not an argument against nihilism. If I want to eat three meals a day, and I want other people not to starve, and I want my wife and kids to have a good life, that's all stuff I want. Caring for other people is entirely consistent with nihilism, it's just another thing you want.
Utiliarianism doesn't solve the problem of having a bunch of contradictory desires. It just leaves you trying to satisfy other people's contradictory desires instead of your own. However, I am unfamiliar with Peter Singer's version. Does it solve this problem?
I think the term nihilism is getting in the way here. Let's instead talk about "the zero axiom system". This is where you don't say that any universes are morally preferable to any others. They may be appetite-preferable, love-for-people-close-to-you preferable, etc.
If no universes are morally preferable, one strategy is to be as ruthlessly self-serving as possible. I predict this would fail to make most people happy, however, because most people have a desire to help others as well as themselves.
So a second strategy is to just "go with the ...
In You Provably Can't Trust Yourself, Eliezer tried to figured out why his audience didn't understand his meta-ethics sequence even after they had followed him through philosophy of language and quantum physics. Meta-ethics is my specialty, and I can't figure out what Eliezer's meta-ethical position is. And at least at this point, professionals like Robin Hanson and Toby Ord couldn't figure it out, either.
Part of the problem is that because Eliezer has gotten little value from professional philosophy, he writes about morality in a highly idiosyncratic way, using terms that would require reading hundreds of posts to understand. I might understand Eliezer's meta-ethics better if he would just cough up his positions on standard meta-ethical debates like cognitivism, motivation, the sources of normativity, moral epistemology, and so on. Nick Beckstead recently told me he thinks Eliezer's meta-ethical views are similar to those of Michael Smith, but I'm not seeing it.
If you think you can help me (and others) understand Eliezer's meta-ethical theory, please leave a comment!
Update: This comment by Richard Chappell made sense of Eliezer's meta-ethics for me.