I think macaws are probably the best bet - they would all be pretty easy to make from a single rig, and they come in a surprising variety of colours and environments.
Scarlet macaw - Perhaps the most famous of the macaws, living throughout Central and South America in both rainforest and woodland ecosystems. They are also among the most commonly-kept of the macaw species, and would be the only Least Concern species of the set.
Military macaw - A Vulnerable species of mostly green macaw, these live in the Andean foothills and Central America in dry forest, deciduous forest and, rather uniquely, in mountainous conifer forests. They are also pretty commonly-kept birds in captivity.
Hyacinth macaw - The biggest of the macaws, a deep blue bird that lives almost exclusively in savannah habitats rather than tropical rainforest. Although nowhere near as common as some other mostly blue macaws (such as the blue-and-yellow), they would add a Vulnerable species with a strong conservation story.
Red-fronted macaw - A pretty widely-kept but Critically Endangered species, which inhabits an area of mountainous desert in Bolivia - in the wild this species nests primarily in holes in cacti. They would add a unique macaw that is slightly smaller than the preceding three species and has a beautiful colour scheme as well.
Golden conure - While not called a macaw, these parrots are very close relatives of the macaws (they are more closely related to the dwarf macaws than they are to other conures). They are Vulnerable in the wild, live entirely in the rainforest biome, have been reintroduced to the wild from captive-bred birds and would add a brilliant bright yellow species to the game.
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My alternative set of birds that could be easily made from one model would be the toucans. They are probably, as a group, birds I prefer even more to the macaws. However, I do have to accept that they are not as common in captivity as macaws are and there are many places with macaws that don't have toucans (I don't think Australia or New Zealand have any, for example). These are the four I would choose that could all reuse the same model.
Toco toucan - The biggest, most commonly-kept and probably most familiar of the toucans, these birds actually live primarily in more open woodlands and savannahs south of the Amazon Rainforest.
Keel-billed toucan - The only Central American species on my list, and also the only one that is not Least Concern (these birds are now classed as Near Threatened). Probably the other instantly recognisable toucan species to many.
Red-billed toucan - This is my favourite toucan species, so obviously would end up on the list - I think of these as they archetypal toucan, with the black and white body and brightly-coloured beak. They are also pretty frequent in European zoos by toucan standards.
Channel-billed toucan - Another pretty common species of toucan in captivity, and also seems to be the species of toucan that smaller zoos keep to start learning how to look after this group of birds. Both it and the red-billed toucan represent different regions of the Amazon Rainforest.
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Another thing that might make macaws better than toucans is that they would probably all be able to have an interspecies bonus - the toucans can actually be extremely aggressive and would probably need their own aviaries. If there was no intention to make the walkthrough exhibits into mixed-species displays, then this problem disappears.
