Well as we discussed in the main thread, I think Behemoths go a long way towards finding those temples.
But don't forget that now Vodyani don't want to explore moons, since they can utilize undiscovered temples - but only if they remain 'officially' undiscovered.

Another idea, might be looking into the possibility of creating a new ship module that essentially allows for anomaly reductions from all ships, but with a 0 production value towards anomalies. Should still allow moon exploration because it cost a turn but no production.

But I'm not sure this is possible, or will work as intended.

Yeah, I was also thinking about some kind of module, maybe only placeable on survey ships.
Since we can explore planets with them, why not moons?

I was able to create a explorer module to reveal explore moons, but it's not completely seamless.
It requires a non-zero production towards anomalies. So I've set it at .1

This makes it pretty unusable for anything other than moon exploration - which is the point (since anything else would take hundreds of turns) but the button still shows up for other anomalies.

All in all, this probably ok.