What you describe will work, with adjustments. (Your schematic shows mosfets which are not connected to ground or the power supply.)
You might want to consider interleaving 3 converters, instead of operating them in unison.
My simulation illustrates a triple interleaved buck converter.
10 kHz, 23% duty cycle.
Each coil carries 5.9 A maximum (give or take). Continuous conduction mode with 31% current ripple.
Notice that the supply does not have to provide more than 6A this way. Whereas, if you were to run the converters in unison, the supply would need to provide 18A at peak.