Been a while but i just had the idea ( well i just read also ) .
Nr 1 the room is small , having a 9000btu airco is def overkill , and it does consume some power (count 750W/h , it will be off a lot but it does cost some money also , and brings some strain on your inverters ) .Better solution for me would be a "ice battery". Icemakers are not more expensive then aircos , they are in fact cheaper ( they are lower power also , and are basically plug and play). Put a ice cube maker somewhere else , let it run , and put the icecubes in the room in a semi-open insulated box . It will cool the room , and you get some free icecubes on daily basis , and on top , if you know after a while how many ice cubes you need , you can run the icecubemaker just for a few hours a day .
Not for you maybe , but i think you can put a battery in a old refrigerator , 2nd hand ... they are cheap , only need to run on lowest setting (highest temp), have metal wall (burn) and keep your batteries at nice cool temp . I know there are selfbuilds around with compressors and evap just need to build the box yourself , but it might take some looking around . 2nd hand fridges are very easy to find