What you and others have said! This is a terrible implementation of trying to combine way too many ideas and honestly just doing it poorly. And why they thought having the pre-recorded stuff being tied to the animals doing things was a good idea is beyond me. Although I do see what they were going for and there is potential. Honestly, if tightened up a bit I like the first 5 minutes. I think Anika as a character is engaging. I think the big problem is where Adam fits in or doesn't. It is like this is a bird show so we just needed a knowledgeable bird guy and trainer to be there so it ends up all being weird and clunky. Here is how I would have written it to fix it:
Anika still comes out first and gives a much more tightened up introduction to Indian culture and sets the place of the great bird sanctuary with the conservation message. Then have the bird walk by, fly by and the land on the arm dynamic interaction. Then Anika would be on one side of the stage tending to something and the attention would shift to the other side of the stage as the UP characters and the male lead/trainer Adam would come around the corner. Through dialogue between Doug and Russell and Adam, we find out Adam is a wilderness guide and bird expert taking Doug and Russell on adventure through India. As they cross the stage they happen upon Anika and she welcomes them and has a comic interaction with Russell and Doug. She also talks with Adam who explains what they are looking for and provides the natural behavior spiel. Anika can tell them that there are many amazing creators here, do you want to go on an adventure and meet my feathered friends?
Then the animal interactions can occur. Where needed Doug and Russell can leave the stage or stay. The big change would be while the bird interactions are occurring there would be no dependent pre-recorded dialogue. Doug and Russell if on stage would be just watching as interested parties. Then as an interaction is complete they can chime in. It seems like the timing will never be right if the actors have to have improv, worry about the animals doing the right thing, and also thinking of the next mark of pre-recorded audio they must hit. Although some of the interactions like feeding the crane can work. Also a big change is that Anika would be the one who knows the birds and their names and is introducing them to a surprised and excited Adam. Anika introduces and names the bird and also tells of the cultural meanings etc, then Adam acts surprised and shocked when the bird lands on him and says hi so and so and explains that so and so is a ________. They do this and gives the bird facts. So the role would be that Adam is a knowledgeable guide for Russell and Doug (a la Guano Joe) while Anika is in her home and excited to share with her visitors her bird friends and tell their cultural story and significance. Makes Adam a bridge between the worlds of Doug and Russell and Anika. Also does a great thing and sets up areas to play off of when things go wrong.
Then end with Doug, Russell, and Adam thanking Anika for showing them her bird friends and how amazing they are. Doug can say he is sad to go but onto the next wilderness adventure. Then Adam can say how there are amazing birds in their own backyards. Anika can end with the great peacock description and the birds back on the stage and scene. So keep the bones, but rework the story around it a bit so there is a better flow to the story.