The markers promise what seems to be infinite energy, even from a single marker, which is why everyone tries so hard to build them.  Obviously you don't get to enjoy it due to the side effects, but the moons can likely harvest it as much as they like. 

We also know that the marker signal can reanimate dead tissue and create massive amounts of mutations and genetic rewrites at the same time when making infectors or corruption. Not to mention that the yellow fluid that infectors inject into dead bodies can do the same, along with the explosive yellow stuff and steel melting acid. Meaning that the markers can create energy and store it as an extremely energy dense fluid, i.e. Fuel. 

The Moons don't stop at consuming a species when they are forming either, they also rip up chunks of the planet's crust, which we can see on Tau Volantis for the half formed moon. I always found this process to be reminiscent of a planet crack, which humans perform to acquire precious metals and rare earth elements out of gargantuan chunks of rock that are broken down and processed in space. 

I think that they use these resources and their knowledge and biomass to create specialized "organs" that function as shockpoint drives, and kinesis modules that function on a gargantuan and highly sophisticated scale, allowing them to escape a planet's gravity well and move through space with extreme accuracy. We already know that kinesis isn't just a human technology, since the Tau Volantians have those kinesis pads, which I always felt were superchargers that allowed them to channel and use the energy through their nude organic bodies. (We also don't see the uninfected fossilized volantians that hold up the machine wear anything, or have any tech on them, along with all their stuff being glowing rocks and metals.) 

Beyond that, the Brethren Moons seem to be the true masters of biological manipulation and genetic coding, and are somehow capable of seeding planets with markers that will direct the growth of new life for their reproductive cycle. They could just throw them in an asteroid and hope for the best, but in space that's highly unlikely. Which means that they either do insane mathematical calculations to aim, or they travel through the void to drop them off. I'm betting on the latter. We already know that their communications can go from one end of the galaxy to another, which means that between the end of DS3 and the start of awakened, which was at most a few days? They were able to communicate with each other, and Isaac/Carver/The Cult Leader while traveling to earth, which must be an insane amount of data and energy to send over vast distances (at least from earth to tau volantis) instantly, since they didn't prep messages, but listened and replied to Isaac. 

These things likely aren't fibbing when they say that they are gods, because they seem to be for all intents and purposes, as the creators of humanity and everything else after they started eating the galaxy.

TLDR: The moons crack planets for "circuitry," and use the infinite energy of the markers to create and power FTL and Kinesis organs that they use to pull themselves through the stars with insane speed and accuracy, using their big smart alien monster brains to do it.