As mentioned in another answer, high speed sync has limitations on available power because the flash must be operated to illuminate the entire image. There are several ways to work around this.
Since you've found that a dark band in the frame is acceptable because you really only need the window, one method is to turn off the HSS. This gives you a tape with the width of the sealing slit at the bottom of the picture, which is correctly exposed by the flash. Experience may tell you if this tape is wide enough for your purposes, but if you do, if you only need to go from 1/200 to 1/500, you should get about 40% of the flash-lit frame.
However, there is probably an easier way to get around this: take a picture with the camera on a tripod with the flash off (for a properly exposed exterior view) and one with the flash on automatically or manually to properly expose the interior and use HDR software to combine the two. This can also be done manually in any image editing program, simply by cutting out the light parts of the window and pasting them into the interior image or by combining them on different levels and using a brightness mask to make the outside area visible through the inside area – an HDR However, the processor is much easier to use and should give good results.
There is also an old-fashioned method that would have worked well with film: add more flash heads and stop, or use a neutral filter to achieve outdoor exposure below the sync speed. This also works for digital recordings. So you don't have to take two pictures with different settings and you can see the end result on the camera screen and make sure you have the shot you want before leaving the room. You may need to do some guide number research to determine how many flash heads you need. However, if you only have one or two stops outside, four will not be exceeded.