On the classic - perhaps there's more to be done with Phistomefel ring? You didn't need to use this explicitly for the competition puzzle - the break in for that was a series of two hidden pairs. However, these are now gone with the removal of the given. I suppose I should also add that the Sudokuwiki solver gets absolutely nowhere with this - in other words this one is off the scale in terms of that measure of difficulty.
On the classic - there's all sorts going on with the larger 2x2 checkerboard combination - but it also seems to me that there's some stuff that limits the permutations within those 2x2s. The configuration doesn't work with a pure 2x2 grid - you need the L trimino cages in order to disambiguate the solution; that said I think they should be working with the larger checkerboard layout in exactly the same way. Or not!
It would be interesting to see if any of my dearest readers is able to share any insight. I would say enjoy, but in this case I'm not 100% sure that experience is guaranteed!
#363 Sudoku – rated 10/10 [Extra Hard]
#364 Killer Sudoku – rated 10/10 [Extra Hard]