My doctor has recommended Xolair for me, which is similar to Nucala. I am still on the fence and haven't tried it yet, but more people have probably tried Xolair than Nucala, and there might be more information out there available for it.
I don't mean to be presumptuous (I'm sure your doctors have covered everything) but just to share what has helped me a bit, I found that the combo of Ipratropium nasal spray, Ipratropium inhaler, and 1st generation OTC antihistamine Chlor-Trimeton helped with my cough. This was in addition to the usual asthma inhalers, non sedating antihistamines, prednisone, and allergy shots.
Good luck with your treatment. I hope you feel better soon. I know first hand that persistent coughing can be a nightmare.