How can I keep a hanging cloth hydrated?
Place the bottom of the fabric in a shallow pan of water. It'll wick moisture continuously until the pan is empty. It should last a day at least, though. 

You could even suspend a wallpaper tray from the fabric itself, which you'd install on the curtain rod (assuming that it's robust enough).



Place a rod through the ends of the tray with the curtain's hem slipped over the rod. It should be stable enough if you only fill it say 1/3 full and keep the rod up high.

Or install a curtain rod at the tray location and hang the try on that.

        _________________________________
       |  ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧  |
=======|=================================|====== &lt;-- curtain rod
       |                                 |           through double hem
       |  ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧  |
       |                                 |
       |                                 |
       |  ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧  |
       |                                 |
     . |.................................| .
   =========================================== &lt;-- curtain rod
     | |  ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧ ♧  | |       through holes in 
     |_____________________________________|       ends of tray 
                                                   or straight rod
                                                   through tray ends 
                                                   and curtain hem