I was wanting to make an entity summon a falling block in the world, which I think I understand how one would do, but I can't figure out how to add a custom tile entity to said falling block. Would the only way be to use readFromNBT and writeToNBT?

Yup, NBT data was the way to go.

Be careful that if you read the NBT saved by one TileEntity into a different TileEntity you will change the position of it (TileEntity.writeToNBT and readFromNBT includes the xCoord,yCoord,zCoord), which will likely break things, so be sure to fix those coords once readFromNBT is complete, or have a custom read function entirely, or update the NBT with correct coords before read, etc.