This is an USDA publication that mentions Monks and IRN's but they also say that, as per the American Ornithologists Union, there are nine species that are now 'officially established' in USA and nineteen additional ones for which there are feral populations but have not yet become established. Looking for more info, I found a list but it has ten species on it so I don't know which one is the one that they don't consider 'established': quakers, budgies, IRN's, peachface lovies, Nandays, mitreds, green and white-winged parakeets, thick-billed and red-crowned amazons. And I have no idea which are the nineteen which have ferals surviving but are not yet considered established although I would assume that the macaws in Florida are one or two of them. I also found a reference to lories, rosellas and hanging parrots but I can't find anything else online.
This is the publication:
https://digitalcommons.unl.edu/icwdm_usdanwrc/2037/
This is the addendum to the American Check List of Birds of 2015 where these species were included:
http://www.bioone.org/doi/10.1642/AUK-15-73.1
And this is a Stanford University paper on Feral Birds:
https://web.stanford.edu/group/stanford ... Birds.html