A very nice puzzle I thought, particularly constructing the centre of the grid like that. Thanks Arden.
I was able to solve the initial four quadrants with only a few entries with multiple possibilities. This wasn't much help for the unclued entries, although a relevant wikipedia article cited an example which does feature. I do hope there's an interesting analytical solution, but I used a script to search for the unclued entries (which are unique).
Converting the first grid to the second was a fun second challenge, oddly similar to a very tractable sudoku.
Thanks Arden!