I am wondering how to securely mount the PCB to a Hammond 1590WDFL enclosure so that the system is watertight and vibration proof.
Typically, for most extruded standard aluminium cases, there are rails on both sides of the case, in which you slide the PCB. Once you close the openings, the PCB can't move anymore.
You see the rails in the middle of the sidewalls. Sometimes, there are several rails, so you can choose at which position you slide the PCB, depending on the height of components.
Edit after WhatRoughBeast suggestion
In order to make it waterproof, you need a joint between the closing panels and the extruded box. Some thin rubber sheet would do. But of course, to maintain efficient RF shielding, you need to take some precautions. Conductive rubber sheets seem to exist, so it may be a solution. Otherwise, additional EMI fingers can also be used to make a RF joint between the sides and the box. Of course, these EMI fingers would have to be attached with some conductive tape for the same reason.
Also, beware of the aluminium oxide layer, which is actually non-conductive. So the EMI fingers actually need to put quite some pressure to ensure electrical contact. And if you go with conductive rubber, you will have to make some tests. If results are not satisfying, you may require passivation of the aluminium to get an external conductive layer, or add some conductive coatings as you currently do with plastic, actually.
And finally, that definitely won't lead to a solution that can be put 100 meters down the water. But if you really need something that can withstand such conditions, this is certainly outside the scope of Electrical Engineering, so you wouldn't have asked here, I guess.