As noted in another answer, High Speed Sync has limitations on available power, because of the way the flash has to be operated to light the full frame. There are a couple ways to get around this.
Since you noted a dark band in the frame would be acceptable, because you really only need the window, one method would be to turn off the HSS. This will get you a band the width of the shutter slit, at the bottom of the image, that's correctly exposed by the flash -- whether that band is wide enough for your purposes is something you may have to determine by experience, but if you're only having to go up from 1/200 to 1/500, you ought to get something like 40% of the frame lit by the flash.
However, there's probably an easier way around this: with the camera on a tripod, take one frame with the flash off (giving correctly exposed outdoor view) and one with the flash on automatic or manually set to correctly expose the interior, then use HDR software to combine the two. This could also be done manually in any photo editor, just by cutting the bright parts of the window and pasting them into the interior image, or even by combining them on different layers and using a brightness mask to let the outdoor portion show through the indoor -- but an HDR processor is far easier to use and should give good results.
There's also an old-fashioned way to do this, that would have worked well with film: add more flash heads and stop down or use a Neutral Density filter to get an outdoor exposure below sync speed. This will also work for digital, so you don't have to shoot two frames with different settings and can see the final result on the camera display and be sure you got the shot you want before leaving the room. You may need to do some research on Guide Numbers to determine how many flash heads you'll need, but if you're only one or two stops over on the exterior, it won't exceed four.