How long do those NTCs take to reset? Maybe that explains why the breaker trips after I turn it back on after a power failure -- if those NTCs are still warm, they would not limit the inrush current.
Modern high efficiency PSUs should have no problem with this, because their active PFC limits input current. NTCs also reduce efficiency and don't work when toggling power, unless you add a relay to short it out. They're a hack.
You need to use an NTC that'll stay within power limit under load to avoid a fire hazard when the relay doesn't work; if you try to do the same with a normal resistor you need large and expensive power resistors.