Your going around in circles.
Like I and others have said said, I doubt they will look at it further due to the physical damage.
As others have said, it’s already been to an authorised Apple repairer, they literally follow the same internal procedures as Apple because Apple wrote them for them.
They won’t be willing to ‘suggest’ anything, all the report is going to say is it has physical damage which will need to be repaired. They will not be able to say if the physical damage caused the fault or not and no one can repair it without fixing the physical damage first. We’re then back to refurb replacement.
Physical and then water damage are the first two things everyone checks before accepting a warranty claim. If either are positive they are will within their right to refuse.
Your only option is to make a claim under consumer law, you have to prove the fault existed at the time of purchase. The normal argument for this is that the device is in pristine condition and didn’t happen in your care. Therefore it must have been there at the time of purchase. Those arguments tend to fall down when the screen is smashed in the corner. You could rely on the report from the 3rd party repairer but it will depend on what they actually say. Again JL could easily argue that the physical damage could have caused it as others have pointed out.
