You can try tillandsias, lots of different kinds available..at least these plants use their roots mostly for anchoring, not really for moisture. Don't even need to put in soil, since they are epiphytic. You can lay them on rocks, or glue them to anything. Depending on the orientation of that window, too much sun may burn the leaves, so just draw the curtains during the hottest part of the day. Just give them some water dunking every couple of weeks during the warmer months or misting on other days to help the leaves.
Pretty much most plants in soil will not thrive well in the long run with poor drainage, unless you use semi-hydroponics, no soil, just clay rocks and put some side holes on the container, that way excess water drains and still a reservoir of water remains below. It will still allow air around the roots. Chlorophytum comosum adapts very well in this set-up. Some orchids thrive in this set-up as well, as long your timing is right when you move them in this set-up.
