I spent 13 years designing electronics of this exact nature: three phase induction motor reduced voltage soft starters and variable frequency AC drives. I spent the last few of those years as a VFD applications engineer helping customers select and configure this equipment for various loads and industries around the country as well.
You will not be able to build something that is cheap and safe. The voltages and currents involved are well beyond the safety margin of a hobbyiest, especially someone who is openly avoiding buying commercial units in order to save money. Don't do it!
While the theory behind AC motor control is very straightforward, the detail level work (heat sink sizing, snubbering, gate drive requirements, de-sat protection, motor overload calculations, bus capacitor protection, etc.) can be quite tricky to get down, especially with heavy duty cycling and regenerative power modes which a carnival ride will CERTAINLY be generating. I strongly caution you against trying to build something of this nature unless you have significant experience not only in microcontrollers and embedded systems design but also significant experience in power electronics and three phase circuitry. People get hurt and killed building this stuff.
My first question for you is whether speed control is really required, or if you only require a soft start up and slow down. Do you vary the speed of the motor once it is started? If not, you may be able to get away with a MUCH cheaper reduced voltage soft starter. These units act like three phase light dimmers; they only adjust the applied voltage to the motor. You will not have a lot of torque at low speeds, but with the right design of motor (NEMA class D) you can achieve exactly what you're after with a fraction of the cost and maintenance.
If you really do need to vary the full-load speed of the motor then you are more or less stuck using a variable frequency drive. As you are aware these are expensive and if you buy cheap you are likely to replace them sooner due to your high surge current (they call this "constant torque") application. What I would definitely recommend doing if this is the case would be to contact various manufacturers (Allen-Bradley, Cutler-Hammer, SAF drives, Benshaw, Yaskawa, etc.) and ask for reconditioned units. Ask for a drive capable of delivering 150% rated current for 30s (this is usually known as heavy duty) or size the drive 30-50% larger than your nominal current rating. You will also likely be running off of generator power which is notorious for being undersized and prone to brownouts and surges as the load requirements change with the state of the equipment being run. Drives don't like that (voltage sags cause current spikes as the motor starts slipping and surges can cause you to overvoltage the bus capacitors) and have a tendency to either fault out or blow up.
I am all about the little guy building something and saving a buck, but this is not the type of project to do this on. If you really want to build a three phase AC drive, start with a little 10HP 480V motor with a hand brake on a test bench. You have all the potential for experiencing the pants-filling sensation of an H-bridge failure or a bus capacitor explosion two feet from your head but without the potential lawsuits and loss of life (except perhaps your own).
I have a suspicion that your problem might have to do with the bootstrap circuit, as detailed in section 5.3 of the data sheet. Some evidence leads to this conclusion:
You are likeley using larger MOSFETs than in the original design (because your overall power is greater), thus you are dealing with a higher gate charge, resulting in a higher current that must be delivered by the integrated bootstrap circuit. It could be that the bootstrap circuit dissipates more power than it was designed for and fails, sometimes resulting in a bad output driver for the high side MOSFET, sometimes taking the MOSFET with it. Adding an external, fast and high-voltage bootstrap diode might help. Note that the calculation in Eq. 9 of sect. 5.3 uses the typical on-resistance of the integrated bootstrap circuit. It's a better idea to use the max. value from table 4 which is twice as high.
Once the circuit goes into overload, you say that the frequency drops. During these prolonged on-times, the voltage across the external bootstrap capacitor might become too low to keep the high side MOSFET saturated, causing it to have a higher on-resistance, excessive losses and thermal overstress. However, in this case, it would be the high-side MOSFET that fails first. Check the voltage across the bootstrap capacitor. A bigger capacitor might help, but this will likely put more stress on the integrated bootstrap driver or the external diode that might be necessary anyway.
Another possibility could be that you are exceeding the maximum slew rates for the high-side driver. This might cause it to do weird things.
Concerning the negative spikes, an external protective clamping diode at each driver's output might help (K=Vout,HS; A=GND,LS and K=Vout,HS; A=GND,HS). Something as simple as a 1N4148 might be enough.
Best Answer
You can try something like this
simulate this circuit – Schematic created using CircuitLab
Set the limit resistor high enough to keep the SMPS from current limiting, and the RC for enough delay to let the motor get up some speed. The relatively slow rise of the gate voltage will allow further motor acceleration during turn-on, but make sure the FET is beefy enough to a) do a good job of shorting the limit resistor, and b) soak up the power dissipated during turn-on.