Zach, some thoughts

Starting current is basically the load of the DC resistance of the
rotor coil(s) when the motor is stationary. eg if the motor was
jammed, the PSU is just pumping energy into a piece of wire. A
technique I've seen but not used is to switch a resistance in series
with the coil to lower starting current. The resistance is switched
out once the motor is turning. Adding a resistance does limit the
available torque, torque which may be needed to overcome
static forces (eg a load) at start-up

A large capacitance on the PSU o/p would supply that extra
ooomph needed to kick the motor into motion. It must be
allowed to charge up, meaning that the start switch would need
to be between the PSU and the motor, not simply turning on at
the wall

Soft-start with PWM to 100% perhaps ?

Or a higher voltage at a lower final duty cycle ? eg 24V @ 50%

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