I had managed to come up with all of the solutions yesterday (except apparently the kitchen pair) and had fit them into the grid. However, it seems I had the NE and SW blocks transposed and, weirdly, they can be easily swapped, yielding two palindromes for the kitchen pair as opposed to the reversible pair I had before. Now the problem is which orientation is correct, since the centripetal pattern of entries allows for two possible solutions with respect to the grid (or 4 if swapping the blocks is kosher). And I have no idea of which Roman numeral is appropriate for the center.