Assuming a NEMA Design B motor, across-the-line starting will result in about 160% of nameplate torque and 600% inrush current. On an inverter, the same 160% torque can be produced with only 160% of nameplate current. Thus the same acceleration time can be acheived with much lower currents and winding heat.
And, even tho constant torque or heavy duty drives are usually rated 150% current for 1 minute, it is important to note that this is 150% of continuous drive current, not motor nameplate current. Since drives are usually rated to NEMA standard efficiency currents and the more common high efficiency or premium efficiency nameplate currents are lower, the resulting motor 1 minute overload rating is more than 150%. And, if that isn't enough current, you can always oversize the drive to take advantage of more of the motor short-term rating (typically 220%).
At any rate, my judgement is that the starting scenario in the opening post will most likely be possible without motor heating problems, assuming accel ramps of more than three seconds and a drive that can produce the current to drive the motor fully at these accel times.