I'm no expert but I'd be willing to bet if you got a power supply with one high current 12V rail--40-60A--it would fix this. It sounds like yours is probably 4 rail.
This is incorrect.
The ATX standard specifies no more than 20A on any 12V rail.
Therefore, to deliver 720 W (60A) a PSU requires at least three 12V rails.
A PSU with one enormous 12V rail is therefore completely outside the established specifications, and should neither be manufactured or purchased.
That said, I use Corsair CX-430 PSUs in my non-gamer builds. Solid PSU.
(It has a single 22A 12V rail that does not trample the Intel ATX specification.)
So do not be put off by PSUs having multiple 12V rails, as per the spec.
More importantly, ensure any unit you consider purchasing uses Active PFC, and is a well-known brand name, well-reviewed, from a popular manufacturer.
EVERY good PSU ever made has been reviewed (at one time or another) on Tom's Hardware and/or [H]ardOCP.
I like OCZ, Antec, Enermax, Silverstone, and yes Corsair but only in smaller wattages.
I can go 22A, 25A, okay maybe even 30A on a 12V rail.
But a 1000W PSU with one single 12V rail? Ridiculous.
Regards