Powering many external 3.5" HDDs (USB) by an ATX PSU
Using ATX supplies as +12V supplies is a well established technique among model airplane enthusiasts -- basically it's the cheapest way to get +12V for charging batteries.
So -- search on that.  They'll have pinouts, and a workaround for the paperclip trick (whatever that is).  If I recall correctly, the biggest non-obvious feature is that you'll need to put a load on the 3.3V and maybe the 5V supplies or the thing won't regulate correctly.
You can get cables that come terminated with barrel connectors, so you don't need to cut up your existing wall warts.
As mentioned in a comment, if the existing supplies are 1.5A, then you can take the 46A output rating of the supply and divide by 1.5A to get the number of drives you can run.  What fraction of the 30 possible drives you actually run with one ATX supply is left to your judgement.
And -- burn you house down, burn your PC up, blah blah -- you've been warned, use your judgement, don't blame me if it happens.