If you don't need to measure below a 10 or 20 Hz, you can use simple current transformers instead of LEM transducer. The transformer should be terminated at best with a zero input impedance current amplifier and the specification checked for an accepatable phase error at minimal frequency.
For the measurement circuit, different solutions are possible, low pass filtering, zero crossing detector and digtal timing measurement is proably most simple. I expect that the inverter current waveform has no low order harmonics, so a simple low pass should be sufficient, otherwise a tuned filter may be necessary.