Extract maximum dynamic range from a Nikon D3400

Every stop you increase the ISO you loose a stop of DR from the highlights.

https://photonstophotos.net/Charts/PDR.htm#Nikon%20D3400

But luckily for you the D3400 is nearly entirely ISO invariant and there is less than half a stop benefit to raising the ISO as compared to just recovering the underexposure in post. And a one half stop difference is barely perceptible.

https://photonstophotos.net/Charts/PDR_Shadow.htm#Nikon%20D3400

So your best choice for maximum DR is to use base ISO and selectively recover the underexposed areas in post. A slightly better answer (.5 stop) is to use ISO 400 instead IF that is enough to retain the highlights you need.

But make no mistake, the underexposed areas will look as if ISO 12800 was used even if you use ISO 100 instead and add 7stops of recovery.

(screen captures used with permission)

All you can really do is exactly the same as you would for a photo: protect the highlights, and lift the shadows in post-processing. In your case, that probably means dropping the ISO.

However, I suspect you may well find the results of doing this with your D3400 aren't of the quality you want, because the sensor has only a limited dynamic range and once you drop the ISO enough to get some detail in the moon, you'll find that the results of lifting the shadows are too noisy. While we very much like to say around here that photography isn't about the gear, it's about the photographer, there are cases when it is about the gear, and this is one of them - full frame sensors do have significantly better DR than crop sensors.