I am not sure how bad the respiratory issues are, but have you tried a REALLY good purifier + filter because, together? There is no way they are a con, as hospitals use them all over the US. Mine (filter+purifier) were nearly 1000 dollars BUT they definitely cut back on dust/ dander A TON (even though with a bird as dusty as mine, there is still more dust, yours are so much smaller and
not nearly as dusty). I don't think you will find many/any worth investigating for under $600--even if they get good reviews (because under that price, they just do not work as well for the level of purification you are after) . Mine was around 650 on the company website, plus the filter and tax. Here is the purifier:
https://alen.com/products/alen-breathesmart-hepa-air-purifier?variant=12172983238723 <- they also have a lifetime guarantee .
According to the website, it is a medical grade filtration system (with the proper filter) and having used it, I honestly believe it.
Here is the filter I use
https://alen.com/products/alen-breathesmart-hepa-freshplus-replacement-filter-bf35-voc
It comes with a pre-filter that goes over the top of the true hepa filter and you can (but don't have to) vacuum it to extend life. The first year I used it (again, 24/7 on the highest setting), I only vacuumed mine around the 6th month of use, and the filters still last a year or more for me.
Here is a fairly recent picture of a pre-filter that I vacuumed (except one square). The whole thing was THICK with white powder (like the square that remains). The microscopic stuff that it filters out obviously cannot be seen, but behind the pre-filter, there is a really elaborate/serious filter (linked above)
***ps-- this picture above was taken after running it for a few months (maybe 2 or 3?) 24/7 on the highest setting (as always)--This
was not taken at the 6 month mark I referenced above*** I've had mine for around 2 years or so and didn't think to take a picture of the 6 month dust lol. Keep in mind, I also run another (smaller/worse filter in the same room, as I often open doors, which means the square footage required becomes higher). Again, a U2 or M2 = dustiest birds out there and so yours will not be as bad.
Now, I don't know if it will work for you, but I use the AlenAir BreatheSmart with the "fresh plus" filter *do not skimp on the filter, as it is the meat of the system*) Never use the sterilize or ionize setting in a home with birds or people with respiratory issues (the birds alone should be enough reason not to, but they can also be harmful to humans to a lesser degree). On the Alen product I have, there is a sterilize/ion setting, but it doesn't operate unless you turn it on manually, so I just leave that off. Also, if power goes off and then comes back on, you will need to turn the machine back on, but in a way, this is good because I was worried the ion/sterilize setting might automatically turn on upon restoration of power (it doesn't).
Alen has a payment plan and I paid around 40 bucks a month- approval was almost instant. Their customer service is really good and the particle filtration for the filter is very good---The filter itself costs $100 (ish) but I run mine on turbo 24/7 and the filter lasts a year with an Umbrella Cockatoo (and they produce AN INSANNNNNNE amount of dust in comparison to either of those birds, although tiels are a powder down bird, they are not nearly as bad as u2s).
Rabbit Air is another very well-respected option that is very good but slightly more expensive. I found this brand because it seemed to be out of my price-range.
You can also buy crazy, hospital grade air filters that are even more intense, but those are in the thousands (plural)
Even if I didn't have Noodles, I would re-purchase my filter and purifier because I see the impact they have in a home. I honestly can say it has been worth every penny---even if it doesn't help with the birds 100%, it makes the air so much healthier because it also removes chemicals and VOCs from the air
**NOTE- it still doesn't make it safe to use chemical cleaners, air fresheners, glade plug-ins, smokes,teflon/ptfe/pfoa/pfcs, aerosols, perfumes etc around a parrot (these should not be used in the same home intentionally), but it makes me feel like I have a bit of a safety net if I accidentally burn some cheese on the oven coils or something while cooking). The filter is easy to change (and they last), plus it is not that heavy and about the size of a large mini-fridge (roughly)
I WILL say,that Alen model it is for 1,100 or so square feet, but you will need more than one in an open-floor plan home or in a home with lost of open doors. I run a cheaper model in the same room with it (HathaSpace) and I have another Hathaspace in the basement, but the Alenair does the bulk of the heavy lifting in comparison. I do NOT think that a HathaSpace alone will solve your problem, but I couldn't afford more than 1 of the Alenairs, so I use these to supplement--
https://hathaspace.com/products/smart-true-hepa-air-purifier (again, while it is decent, it is not on par with the Alen)
I guess if your daughter does have serious respiratory issues, I'd say this could be a really good thing for her in general, even if it doesn't solve the bird problem, it certainly has a MASSIVE impact on indoor air quality...so if you have the funds, I would try it (because with or without birds, indoor air quality can be a serious issue).
Having used MANY cheaper purifiers ($50- $350), they do not hold a candle in comparison-- you can't judge high-quality purifiers based on experiences with machines under that $600-$1000 range (I am assuming you were running something very basic, like a germ guardian or another cheap model--even the Hathaspace I have is not sufficient by itself, despite glowing reviews on Amazon).
I do not work for Alenair or anything, nor do I represent them in any way. I just have been really happy with mine and it isn't very loud. It also has air quality indicator lights and they are SUPER sensitive compared to others that claim to have them. Hathaspace machines have this too, but they are so much less accurate. Last thing- there is a filter warning indicator that turns yellow a few weeks or even months before it turns red and needs to be changed (so that is also helpful).
They also capture something like 70% of viruses--- here is a link to how AlenAir has been used in school reopening in CA
https://alen.com/blogs/news/press-release-back-to-school