This paper is two years old now, but still seems big news to me:
Genetic complexity, roughly measured by the number of non-redundant functional nucleotides … Linear regression of genetic complexity (on a log scale) extrapolated back to just one base pair suggests the time of the origin of life = 9.7 ± 2.5 billion years ago. … There was no intelligent life in our universe at the time of the origin of Earth, because the universe was 8 billion years old at that time, whereas the development of intelligent life requires ca. 10 billion years of evolution. (source; discussion; HT Stuart LaForge)
That seems remarkably close to the age of the universe, 13.8 billion years. Yes it might be a coincidence, but we have other reasons to suspect life began before Earth. So I take this as a substantial if hardly overwhelming confirmation.
You write, "Since horizontal transfer probably doesn't work so well in multi-celled organisms".
That's true, but it's by design -- the cells of a multi-celled organism can cooperate only because they "know" that their neighbor cells are genetically identical.
The times are in the 20th century for the most part. We have no clue what genomes bacteria had a billion years ago.