Ivomectin works on invertebrates, it inhibis the way sugars (glucose) is metabloized. It is very effective for killing all inverts, (worms, earthworms in the garden will be harmed by using the poop containing it - so compost it for at least 6 months to break most of it down, also kills all the mites, lice, and virtually all the parasites known, works great on hard to get worms in the tissues, lungs, liver, eyes, blood, brain, etc. The greatest problems people have found is that it is soo darn effective that an animal (or person) heavly infested can have a reaction to all the dead parasites and die from that!! They started to give people steriods and antihistamines to prevent this in heavly infested areas. Unfortunately as with all chemical cures, we are starting to see resistant parasites, but that always happens with chemical remedies.
So what to do?
Birds are vertebrates and should be relatively safe to medicate with this type of chemical, in other words, it has a large margin of safety on vertebrates. I have no experience with the dosage, but birds are tiny so the dose will be small. Personally I would try it out on one bird to see the effect, next day if all is well, dose more. Be cautious and careful, keep a record of what you tried and how it worked.
I liked JayDe's idea to dilute it and then give 2-4 drops on the back.