Currently, it looks like The Beneath supports modded worlgen using onChunkPopulate:

It would be great if you could add support for modded cave gen as well.
Currently, cave gen for The Beneath is initialized at declaration:

Instead, maybe something like the following could be done in the constructor:

public ChunkProviderDeepDank(World worldIn, long seed)
{
    ...
    genDankCaves = new MapGenCavesDeepDank();
    genDankCaves = net.minecraftforge.event.terraingen.TerrainGen.getModdedMapGen(genDankCaves, net.minecraftforge.event.terraingen.InitMapGenEvent.EventType.CAVE);
    ...
}

I haven't tested this, but I would think the actual fix would be similarly simple, if not exactly what I wrote above.

Let me know what you think!

So, can we use Yung's Better Caves with The Beneath 1.7.0? I'm not seeing a cavegen config option documented anywhere but a cursory glance at the commit above suggests that enabling third-party worldgen is sufficient.

Yes, enabling third-party worldgen does the trick.