Do you use the paid UVpackmaster2, or the free (i think?) old version? Considering giving it a try.
So would you still say that I should join all the different objects in the scene into one ‘object’ / mesh, and then do a UV unwrap for each material?
Just trying to get my head around the ‘best practises’ workflow. Should I actually merge the different objects, or just ctrl-J them so they appear in the same object selection? (Not sure how the overlapping spheres might cause issues when textured)
I use the paid for version. It’s worth every penny. No, I don’t join all objects into one mesh. Simply select all the objects you wish to share the same UV layout (typically they would share the same or similar materials), enter Edit mode and unwrap them at the same time. When it comes to getting it into Substance Painter there are several options, select everything you want and export an FBX with Selected Objects ticked in the save dialogue or use the Xolotl Substance Painter Live Link addon.
Each material will be treated individually in SP and will generate its own set of texture maps for bringing back into Blender. For that reason another workflow can be to use temporary materials in Blender to create an ID Mask, then assign a single material to everything. In that way you can use the ID Mask to separate stuff in SP and end up with a single set of PBR textures for everything.
My original plan for that raygun project was to have everything in one UV map, but different materials. I had planned to either manually combine all the diffuse maps, all the roughness maps, all the normal maps, etc., later in Photoshop or using a utility I think I found. I ended up not bothering as my PC was happy enough rendering the shots. You can also use Substance Designer to combine the maps from several PBR texture slots. I need to make use of Substance Designer more often.
For your intersecting spheres: I’d say give it a try. Personally I’d boolean them together in the modelling process and do all the clean up required.
Oh… If you were wanting a decent guide to using Substance Painter with Blender, CG Boost have a good training course which covers a lot of ground. I’m not sure how much it costs - I won a membership in a contest, but it covers a lot of what you need to know and has a lot of tips and ideas too. The example project they are working on is even a sphere based sci-fi thing 
16 of the lesson files are available to watch free as well if you want to get an idea of what the course content is like.
Have you applied the scale on the high poly?