Hey guys. I ended up going for for the Seasonic Prime Ultra 750W in the end. It was significantly more expensive than the others but I don't regret it at all, it was a dream to actually work with.
Anyway, the big news is it's had no effect on the 2080 Ti, it's still refusing to display a signal while running the fans at max as soon as I turn the PC on. I picked up a VGA cable as well so I could actually get into Windows and see what was going on with the integrated graphics, and I found that the GPU isn't even being recognized at all. Regardless of that I tried to install the latest Nvidia drivers like GordyR suggested but it refused to go through with it because I had no compatible components. Meanwhile, the old R9 390x is still working perfectly with this new PSU.
So yeah, looks like I'm going the RMA route.

This is the first time I've ever had to return a part after 5 PCs, so I guess it had to happen eventually. Is it likely I'm gonna have to wait a long time for a replacement because of the demand?