Here is another approach: Table 430.22(E). The application is a sump pump, and the on/off cycles are driven by water level. I watched the existing system operate a couple weeks ago. It seemed to me that it took less than 2 minutes for the pump to bring the water level from the "on" setpoint level to the "off" setpoint level. Under worst case conditions, I am made to understand that the pump would cycle on every 11 minutes or so. We are looking at ways to extend that, so that the pump doesn't experience that frequent a start/stop cycle.
With that said, I think I can use the "intermittent duty" 15 minute rated value of 85%. So my minimum ampacity would be 85% of 124, or 106 amps. A #2 would do that job. I would still have to deal with VD issues, but this could resolve the "conduit fill" problem.
Any comments?