Question: Looking for a book I read in the late 60s: humans were almost eradicated in the galaxy but discovered technology that made them almost godlike. They then lived in miles-long spaceships and watched over races in the galaxy as "guardians".

Answer: 
I think this is [*Crown of Infinity*](https://www.isfdb.org/cgi-bin/title.cgi?22315) (1968) by John M. Faucette. It was apparently only published as an Ace Double with *The Prism*:

[![Cover of the Ace Double "The Prism"/"Crown of Infinity"; "The Prism" on the left shows a man in a leather shirt and skirt swinging a long sword two-handed at a human-sized bat-like creature with arms as well as wings; a deep, jagged crevice splits the barren, rocky surface to their left.  On the right the cover of "Crown of Infinity" shows a dark spaceship, in the form of a pair of globes connected by an open cylindrical framework, in battle with 6 other silvery ships that are collections of complicated curves.  Orange lines of light shoot out from the central ship, and are striking some of the others.  The background is vaguely nebular, with the light of stars glowing through a sky that shades irregularly from red at the bottom to blue at the top.](https://i.stack.imgur.com/mpupV.jpg)](https://i.stack.imgur.com/mpupV.jpg)

Unfortunately I no longer have my copy but I remember humanity almost being wiped out in sneak attacks by various alien species uniting....led by lizard like creatures.

Then there was a generations long hunt and destroy programme but humans proved really good at sneaking around the galaxy and surviving, any time a ship was destroyed signals were sent out so other humans could avoid that particular fate.

Slowly the survivors increased their technology until they eventually reigned supreme and took their vengeance - after that they oversaw the galaxy and became known as the Star Kings.

Note:- as I said, this is from my memory only - please anyone, feel free to edit if you have a source

There is a [review on Goodreads](https://www.goodreads.com/review/show/53040173), and [another on Amazon](https://www.amazon.com/gp/customer-reviews/R163I6F7EW6Y0T/ref=cm_cr_dp_d_rvw_ttl) that have broadly similar details.
Your description is very similar to the plot of [The Lensman](http://en.wikipedia.org/wiki/Lensman_series) series by E. E. "Doc" Smith. Intelligent species on many planets are part of a breeding program by the Arisians, one of two competing galactic races, which results in superior humans and other species. With the use of a "Lens" provided by the Arisians, which provide telelpathic powers, the super humans form the Galactic Patrol to enforce laws and keep the peace in the galaxy.