well, speaking of topweight......
did the ships have a lot of stability reserve? because margin of displacement says exactly nothing about the ships stability.
removing the turrets, the magazine, the conning tower....... the issue might actually not be to be the ship stable, but to have her lay as she should do, without the weight in the places it was designed to have it.
I have not researched or looked at this ship to say if she would work or not, but the new directors will be quite a bit heavier then the ones already there. the removal of the magazines in the hull brings the topweight up as well, but here the displacement margins can come in useful: you can ballast to compensate. the radars, high up in the mast, have a lot of effect because they are high up. so, your center of gravity might well go up
however, looking at the albany class, which IIRC was build on a hull related to these, I think it might work.
I am not entirely certain if it is an good idea to surround magazine spaces of the Mk 10 GMLS with aluminium btw, there are some drawbacks on that.
last but not least, I think you would loose very little weight in armour, as the armour was quite integrated in the ships design as far as I know, so removing armour would have structural effects as well.