How big is your aviary and how long can you quarantine the new bird in a totally separate space? In general, mixing species can get very tricky (unless you have a massive aviary and a very proper knowledge of the birds themselves)- 1. they can have dander that irritates the others (if you mix old world and new), 2. parrots can be serious transmitters of deadly but asymptomatic diseases, 3. When there is a size difference, a snap from one can kill the other, and 4. the body language is conflicting across species...not to mention the fact that one bird would fly somewhere 30- 40 miles a day in the wild, so putting a ton in a cage isn't really entirely fair--especially when you add in another species. I will not say that no one has ever mixed species, but I personally think that it is very risky in the space that most people have when they they say "aviary"
An eclectus parrot would NOT be suitable to house with budgies. An eclectus has a very different diet from budgies and is more than triple their size. There's some debate if harnesses are safe for smaller birds but harnesses are made for them and they can be trained to wear them.
I honestly don't know how an Eclectus would go in the company of budgies. Budgies are, as my bird vet is fond of saying, "like that pesky little brother who just doesn't know when to quit!", and this can get them into trouble especially with a larger bird. Therefore you need a species with the patience of ALL the saints to prevent injury to a smaller but very feisty bird like a budgie. I'd say cockatiels are probably your best bet!
I play videos on youtube-tv for my budgies, and many of the multi-hour "budgies in an aviary" videos, include cockateils in the same, VERY large and spacious aviary. I have Not seen any aviary with any other combination, only Budgies-Only, or Budgies & Tiels (with Lots of space).
Strongly recommend not mixing budgies with Any larger bird (other than 'Tiels), in its living space. My budgies have free range of my living area, including full access to Sunny's cage -- WHEN i am home with them. My Sunny is really calm and well-mannered, and when Jefferson-budgie oversteps boundaries, Sunny just Looks at me, like "REally???,: and kinda rolls-over on top of him.
BUT I would Not allow my budgies access to Sunny's cage if I were not home.
Budgies are well-known as beaky little brats occasionally, and your little Napoleons can get themselves killed taking on a larger-beaked bird.
I agree with Hannah and Fiddlejen. If the aviary is not big enough, do not try to mix species.
I guess, aviaries with a fair living space can have finches and budgies. One parrot that might do well with budgies is the linneolated parakeet. They are quite calm and friendly in general and are not much larger than a budgie, smaller than a tiel.
Please consider that different species have different immune systems. What is not that offensive for some species can be lethal to others... Unless the aviary is kept highly clean, this could be a problem.