Why have the Abrahamic myths become so popular? What is different about them?

"the Abrahamic myths" That's rather broad. It's not like they agree on much between them. Romans, Europeans, American settlers. That covers most of the Christian bit. Judaism is not very popular at all, nor has it ever been, and Islam is a different story than Christianity but with the same theme of conquest and forced conversions, followed by historical inertia.

They were constructed for the purpose of social control and have had 2,000+ years to perfect the practice.

They have been spread by the sword and the gun. The Arab conquests, the Crusades, European and American imperialism. And let's not forget those wonderful Zionists and how they stole Palestine, and are still trying.

Popular? Hardly! They were imposed upon the citizens of the "Holy" Roman Empire to subjugate them.

Writing. Really helps with transmission to other cultures. Look at Judaism, two distinct cultures (Roman and Arab) appropriated and mangled our written tradition but completely ignored our oral tradition. It's their reworked versions which have become popular. Few people are even aware that Jews read our own texts quite differently. As for other cultures, read some of the classic Greek myths and then watch some old films and read some great literature, you'll see a lot of common elements and plot lines. If Greek myths have finally died out, it's only because of the dumbing down of mainstream culture in last few decades. Though I suppose with the right editing, a fair bit of reality tv could be turned a tragedy about hubris....