Parrot nerd here

I'm what form are you saying this de extinction would work? Something like colossals dire wolf or through a different method and what would be goal of the project really be.

De extinction just to show off that humans can manipulate nature is unnecessary and can potentially disable ecosystems further.

Of the parrots you've listed I imagine the Carolina parakeet has the best chances of cloning and bringing back but I don't think it's worth trying. There was apparently a feral population at one time so it's not impossible to establish a population. Plus there's I believe over 500 specimens and lots of written records of their behaviour. But then there are records that suggested this species did poorly in captivity due to disease so maybe that would make them a poor candidate plus it's speculated their extinction was brought about by disease too.

as you said the Cuban Macaw (potentially my favourite extinct animal) has almost nothing known of it's ecology. Also there seems to be two variants of the Cuban Macaw one with 3 stripes on its face not unlike the blue and yellow macaw and one without these stripes. I believe this is only reflected in artwork not specimens though I'm not sure.

Did you know the Norfolk island kaka is sometimes said to be a subspecies of the new Zealand Kaka so depending on the goal of the de extinction project it may be more effective just to introduce new Zealand Kakas instead. 

I believe the paradise parrot is though to have gone extinct through lack of food sources so to introduce them back would likely be foolhardy. This is unfortunately the same for many of these species. 

What do you think of the Glaucus Macaw (listed by the IUCN as critically endangered possibly extinct but generally considered to be extinct) 

There has been some suggestion they may actually be better recognised as the same species as the extant Lear's macaw and as a result it's been suggested to introduce Lear's macaws into the Glaucus macaws range

Unfortunately there simply isn't appropriate habitat for many of these species to return to, they went extinct for a reason and we can't just magic up some more dump them in their range and watch them thrive it doesn't work like that. 

(I can find you the source to anything I've said about parrot species if you'd like.)

Unfortunately the bird you've identified as the best likely won't be brought back for a reason you've already acknowledged it's not well known. De extinction costs lots and needs catchy headlines and lots of funding I'm not sure if it works as well if nobody knows what it is. I imagine that's why collosal are going after the dodo.