ok, so it looks like the screen is a BW variant 7, which seems to be pretty common. Easy enough to make it work on 5V, but I'll do that later, screen itself is working fine.
I have noticed that this aftermarket case is not made very accurately. You can see an example as to why here:

Original screen cover that came with it

Gorilla glass screen cover
It'll still look fine if I align it accordingly as good as possible, though.
I then started doing all the modifications needed to the case:

Removing unneeded screw posts and preparing to drill X and Y button holes

Removing a chunk of the battery compartment, because the battery coincidentaly fits really well otherwise:

If it all fits like that, I will leave the compartment like that. If not, I will come back to remove more.

Drilled X and Y button holes and roughly cut off the screen area with a saw.

Removing more material

Testing look of the gorilla glass screen surround