Update: The patch, after installing it according to its instructions sadly didn't help. The last thing I tried was putting both games on the same monitor, just layered on top of each other and the issue persists. Since it's a small window I usually prefer to have it on the same screen anyway, rather than another monitor. The only half solution I found was, if I opened a browser (e.g OperaGX) with the game (in this case, WoW) in the background, the issue is still there UNLESS I open CiC when I have Opera in fullscreen and WoW tabbed out in the background. So long as I keep CiC in this fullscreen browser tab, I have no issues moving or resizing the window and can switch freely back to WoW. But if I layer CiC on top of WoW (or any other game) that's when it'll crash if I ever need to move or resize the window.
My second monitor is usually for work since it's got very crappy colour grading and a weird aspect ratio, so it probably wasn't worth mentioning I used one earlier. Since CiC would usually be taking priority when I'm on my main monitor.
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Sorry to hear the patch didn't work, but am I reading your comment correctly that you are playing the game through a browser, and not the windows exe version? You said it worked if you kept CiC in a fullscreen browser tab, so I'm just curious there, because if that's the case then it I would also suggest running the exe version instead of the web version and seeing if that helps. Otherwise, I think you're stuck with your Frankenstein solution you described there, because I'm stumped with this one.