"Conservative Christian logic:
1. Killing babies is always wrong
2. God can not [sic] do anything wrong
3. God kills babies"
"Correct"
So you admit your logic is contradictory, because that is a logically flawed argument.
"God has condemned EVERYONE to die"
People die because we are biological organisms, and all biological organisms eventually die
"Everyone dies, one way or another, therefore God kills everyone"
If god exists, then yes
"God, Who is perfectly righteous and just, can kill anyone He pleases, and He would be right in doing so"
According to whom?
And if that is true, then that poses a big problem for you. Here's why:
There are times in the Bible where God tells people to kill other people (commanding the Israelites to kill the Canaanites, for example). So God can possibly tell someone to kill another person. If someone kills a person and says god told them to do it, how do you confirm that God really told them to?
"This same God is also perfect in love and mercy, and has paid the greatest price imaginable, so that no one need die the ultimate death, the second death"
That's what many Christians believe. I don't accept that statement as true.