Reading this thread just YANKS on my heartstrings so hard. I lost my beloved, sweet little cockatiel to a prolapse caused by constant egg-laying.
If you CAN get her into a vet sometime in the future, do. The prolapse doesn't look like it's all that bad right now, but it can get so, so much worse. The first time Tsuki prolapsed, it was a lump maybe the size of a marble or a little less. She had a stitch put in her cloaca for a week or so to prevent further prolapsing or damage.
The second time it happened, it was... well, a lot bigger than a marble. More like a shooter marble, maybe. A fair portion of my little buddy's organs were outside her. We had to rush her to the nearest emergency vet, the only one open on Sundays... and it was an hour and a half away. She survived the drive, they tucked everything back in the best they could, but the damage was too severe. She was perfectly fine the day before, and when we got up to check on her, she was like that. It was, I believe, over a year since the first prolapse had happened. We'd spent that whole year trying to get her to stop laying.
I wouldn't wish that fate on anyone's bird, nor would I want any person to have to see their bird in that state. It was terrible. I still have nightmares sometimes, wondering what I could have done differently. I had never heard of vitamin A being a potential problem! I hope that helps. :C One egg a month sounds like it could be manageable. My birdie would lay double or triple clutches at a time, sometimes more, and rarely went more than a week or two without laying. Even hormone injections (at $100/month!!!) only curbed the behavior.
I was in touch with a specialist about getting her spayed, but they eventually decided they wouldn't do it, as she probably wouldn't survive the procedure.
I can try to suggest all the things I've thought of since Tsuki died, all the things I wished I'd done differently. It sounds like you're already doing a lot, though.
Photoperiod is important. Longer hours of darkness can help curb the hormones that drive egg-laying.
ANYTHING you can do to knock the bird out of her comfort zone a little can help with nestiness, too. I rearranged Tsuki's cage and moved it all over the house, but she was unflappable (bird pun unintended). After a day or so, she'd be back to it. Putting the cage outside helped, but that's only good for summer. And my vet didn't want me to do that without a mosquito net because of West Nile. Before the net we ordered made it to us, she had died.
I wish I'd gotten her a new cage. I don't know how long that would have helped. But it might have made a difference. I don't know if a sleep cage would have done much for my bird, but it could be worth a try.
Teaching foraging skills might also give a bird something else to be focused on.
Good luck with Munch. She's so cute. Egg laying is SO stressful to deal with. I told the breeder I'm in touch with that this time I won't have a female. Maybe someday, if it were a larger bird less prone to this. But for now, I just can't even run a small risk of going through that again. It's awful, and I totally sympathize with you. Keep us updated and know I'm sending my best wishes to you!!