Need help with loose Gillette Milord

[moshulu]

Guy wants to sell me a Milord. It has some cosmetic problems, but the main issue for me is that the doors remain loose even when the TTO knob is fully tightened. Not much: maybe a millimeter or so of play. When I insert a blade and screw down, nothing moves any more, but that doesn't really reassure me. My question to the experts is: is there anything I can do to get those doors to close correctly? Thanks for any advice.