I am sorry to hear about Newt having this uncommon and difficult disease.
My name is Rebecca. I am a veterinarian, and will do my best to help.
Many cats with condition have low potassium. Is he taking potassium supplements? Is his potassium normal?
There is a chance that giving him steroids will worsen the hyperaldosteronism symptoms and blood pressure.
If I were going to try giving steroids to a cat with this condition, I would use a short acting form of steroids, like dexamethasone sodium phosphate. That way, you would get the anti inflammatory benefits, but the drug should be out of his system in 24 hours. There are some forms of steroids that last for days, even weeks, that should definitely be avoided.
I am not seeing responses from you. I hope you can see what I am writing.
I will try to connect with you another way, if I do not hear from you soon.