Each square meter of moon receives a time-averaged sunlight input of about 340 watts [1]. The surface area of the moon is 3.79 * 10^13 m^2 [2]. The most efficient silicon solar cell is 27.6% efficient [3]. The gravitational binding energy of the moon is 1.2 * 10^29 joules [4].

Putting all those factors together, gravitational disassembly of the moon will take

(1.2 * 10^29) / (0.276 * 3.79 * 10^13) = 1.15 * 10^16 seconds, or 364 million years.

It will take longer if you model the moon as a shrinking core where all sunlight collection and replication takes place. It can go faster if the replicated units become part of a Dyson swarm beaming power down for disassembling what remains of the moon.

Gravitational disassembly of the moon in 8 years requires an average power of 476 exawatts (10^18 watts). It also seems like you would run into thermal limits trying to turn the moon into more clanking replicators, even if you did have exawatt scale beamed power from your Dyson swarm; you can't beam so much power down that the replicators melt from waste heat before they can finish building.

[1] https://en.wikipedia.org/wiki/Earth%27s_energy_budget#Incomi... -- Earth and its moon are roughly the same distance from the sun, so Earth's top-of-atmosphere solar input is a good approximation to the moon's surface solar input.

[2] https://en.wikipedia.org/wiki/Moon

[3] https://www.nrel.gov/pv/insights/assets/pdfs/cell-pv-eff-cry...

[4] https://www.universetoday.com/121421/how-could-we-destroy-th...