We just installed a few VS (Variable Speed) inverters for some pump motors. The drives use a 24 VDC digital input for their RUN command. I just hung a few hour meters across the RUN lines. Next, does the motor control panel have a lamp that indicates the drive is running? There might be something there you can use. What commands the inverter to run?
If the start / stop buttons are standard 22mm or 30mm operator type that use contact blocks, then you could get a NO and NC block and add them as you suggest and add a DPDT 24 VDC coil relay. Then run the hour meter off that as you mention but I would be looking for something simpler first.
Ron