My sweet kitten has a strange purr

My female kitten, Sweetie, has always had a strange purr ever since I got her at 6 weeks old (she's about 7 months now). She purrs so much, her purr turns hoarse and dry, and she ends it with a single cough. Ever since she was a tiny kitten, she’s had a very loud and long purr (she even purrs at the vet). It just grows so loud and hoarse, it sounds painful. You can hear her purr from across the room. We almost avoid petting her because it sets off the purr-to-cough sequence. But she loves affection and still randomly purrs without any interaction.

We’ve taken her to the vet for xrays. They only noticed a "shadow" indicating a slightly enlarged heart, but even that was not for certain. They threw around a lot of diagnoses (lower lung disease, mildly enlarged heart without evidence of decomensation, cardiomyopathy, congenital heart disease, asthma) and she went on antibiotics for a few weeks and is now on prednisone steroids. It does not seem to be improving, nor is it getting worse. She’s about 6 months old. 

They recommended an asthma shot (turbutaline) and getting an EKG. The EKG is really expensive and it seems to be more of a shot in the dark than a “next step.” I could be wrong, though. She's the sweetest cat of all time and just loves being pet, but how hoarse she gets from purring seems really painful. They said if it is a heart issue, there is nothing to be done and she will just have a very short life (1-3 years max).

Anyone else experience something like this? Not sure if it is just how she's built.

video

https://reddit.com/link/1hobbqh/video/o7lxp6jvqm9e1/player