That is going to be a challenge with the complexity of the single object that spans all the spheres.
For such a structure I might recommend:
- Create a tile that include 1-4 spheres and a small section of the large surface. Then array the resulting tile to get the size of the fina object needed.
- For highly complex Boolean structures, the plugin Isopod is able to do this quickly and have the results that are 3dprintable: Isopod - implicit surface tools
Those are the best two strategies I have seen work for these types of models.
