i guess you would have to explain a bit more what the intentions are, is it for a student project that will other than for this purpose have no further manifestation and as such will not fail if the tilings are not 100 % production ready or are the tiles an integral part of your project? would you want the bottom to be entiled either? meaning the entire surface covered?
either way the tiling would have to be rethought then. i am not on the computer now but i would suggest to start with one tile on the bottom intersect it with the structure and pull the rips up along as curves to get an idea if it works for you