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I'm okay with leaving the diagram as it is, if it's not too objectionable. I tried changing the Border Size using the Diagram Designer as suggested, but only the outer left and outer top border were affected, i.e. otherwise not at all changing the thicker spacing between the small 2D boards (which I called mini-boards). At least I was able to make much use of the HTML code string I had pasted earlier into my webpage submission page, by cutting & pasting the part relevant to the FEN string, when using the Diagram Designer from scratch (I deleted certain parts & replaced then with '/' where I had to, though). I did something similar in the way of cutting & pasting the file and rank labels. Otherwise I had to set the fields (e.g. for the number of Columns) from scratch again where appropriate. The whole process was not nearly as time consuming as when I generated my diagram the first time from the Diagram Designer.

In spite of the above, I am wondering if there is an existing or unwritten convention as far as how the checkering of the 2D boards alternates. Almost all the webpages with 4x4x4x4 4D chess variants on this website were submitted to have the checkering alternating kind of like in your example, Fergus, much like there is a convention for this in 3D chess variants apparently. Still, I did notice one 4x4x4x4 variant on this website that had the 2D boards checkered the way I have them at the moment (some other such 4x4x4x4 variants had diagrams that used no colours for checkering at all!). As I say, do you or anyone else have strong feelings on the checkering of the 2D boards? Personally, I found calculating when playing decades ago using the checkering I have for 2D boards to be natural enough in that it did not offend my sensibilities somehow, at least.