Source of 5v power on a typical motherboard
The ~120 - 150W limit on +5V rail in desktop ATX12V power supplies is dictated by economy - it is difficult to find cheap rectifiers with > 30A current.

But you might find plenty of power on 12V rail. Since your load is distributed over "a bunch of 5V devices", you can use distributed converters. What you can do is to use (make) a bunch of in-line DC-DC converters to convert 12 V into 5V, one per each of your 5-V devices, or whatever your load is. The converters can be encapsulated and are easily available with 3-5-10A load capacity. Something like this one, 



This should solve the problem of insufficient 5 V power.