Don't work over anything especially the hook till you have established where exactly things are interfering.
Smoke the bbl as others have said and carefully place it back on the frame and close it. Back it off and examine.
One thing I do see that might be a problem is that the front edge of the bbl flats is hitting the frame flat (water table) before the bbl can sit all the way down.
The bbl can't pivot & wrap it's way around the bbl flat. It should come down on it.
That faint line straight accross the bbl flat even with the hook is probably the impression of the front edge of the frame flat(s).
It may or may not be interfering,,that's what smoking and checking the fit is all about. But it's something to look for.
Relieving the hook contour to fix that will allow the bbl to sit higher for sure. But at the expense of a sloppy hinge joint where the hinge pin is round and the hook is then oval shaped.
Go slow, look for the tiniest interference betw parts. They don't always jump out at you as large bright spots rubbed off of the smoked part.
Don't forget to check the bbl rib extension for interference in the frame cut too.
Take the extractor out of the bbls while doing the initial bbl fit. It looks like you have already,,,You want just the bbl and the frame to be fitted.
