@akaheisenberg – I understand how frustrating this is for you. You have kept exceptional notes!
You are on the right track I think.
Endoscopy was normal, but they saw abnormal vocal cord position.
Upper GI done- I assume they did a Barium swallow, observing live how the esophagus moved. All normal, right?
Did she ever have chest X-ray and/ or chest CT?
I agree that she may have aspirated and may still do so. The vocal cords may have been irritated from that. Less likely with vocal cord paralysis.
She probably started out with GERD- quite common in infants.
Next step for you is find the best children’s hospital.
Keep us posted on researching where to go!