Enough time has passed for me to collect myself over this infuriating issue and circle back with this group. After pleading with Tech Support by phone and chat over the course of several days, below is the best response I could garner:
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**[Private conversation removed in line with the Community Center Guidelines]
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I'm seeing red reading this again (referring me to a general help article after admitting nothing will change the order?). Ahem, moving on... I painstakingly managed to fix the issue of the "Where you'll sleep" bedroom order on my listing...
I began by deleting every photo and reuploading (this proved unnecessary in the grand scheme of things), testing each change along the way on the live site. The problem arises about halfway through assigning photos to the appropriate room in the "Rooms and spaces" section. Nearly EVERY change you make after this will reorder the bedrooms, sometimes other rooms too. I spent 2 HOURS (my activity log will prove it), making random changes until it FINALLY settled on the correct order (bedroom 1, 2, 3, bathroom, etc. with correct bed sizes).
I'm happy to report my listing has maintained the correct order for more than a month now. The problem is, I can NEVER make another change to this section (I have threatened my co-hosts to never enter this area, lol). I wish I could tell you I identified some pattern or easy fix through all that trial and error, but the order it places the rooms is completely random. However, I can say that it will assign bedroom 1 to the first position < 5% of the time.
Mind you, this is specifically addressing the order of the "Rooms and spaces" (backend) / "Where you'll sleep" (live site) part of the listing. Airbnb continues to randomly rearrange my photos in the "Photos" (backend) / mosaic layout (live site) section. I've given up on this issue.
Good luck to others. If you find a few hours on your hands, you can try out my method and see if it works for you, too. Please share if you find a better fix, as obviously Airbnb doesn't recognize this as an issue so it won't go away anytime soon.
P.S. One final thought: Tech Support's response suggests the heart of this issue arises from having photos of different orientations (landscape and portrait). Personally, I am not willing to delete all the portrait photos from my listing just to maintain the order I have set. I'm not convinced that having photos of only one orientation would fix the underlying issue, anyway.