I was more thinking if the trans is calling for TC lockup at too low an rpm it would cause the surge and if you’re building that much more boost outside the turbos map, could be causing the barking.
I have a 15ss, 7x.085’s, hx35 and a boost elbow and most boost I see if 33-35. Sounds like you’re wastegate or boost elbow is jacked up. I just wouldn’t be so quick to say new turbo since that’s not a cheap fix. I’d be trying to figure out how to control the boost and see if you’re having the same issues and try and save some money. If it turns out it is the turbo, at least you’ve checked everything else (read: the cheap stuff) first!