The motor is going to run hot, but as long as the cooling fan does the job, I think you're on the safe side. What I'd recommend is to look at the fsw switching frequency in the inverter. Try to work with the minimum possible setting (2kHz, 4kHz), more than that you're certain increase the losses into the motor (and the inverter). Are you going to run in encoder or encoderless vector? Not all the inverter manufacturers can work in an optimized way at low speed, I'd check that first. But as you're going to cool down the motor with the fan, I expect the stator and rotor resistance to remain stable, which should help the inverter to control it at this low speed.

You're looking at a large scale science fair project, since the inverters by listing and code require grid time base and voltage to be within limits before they operate - modification of this would be dangerous. You could theoretically construct a means to switch the PV array output off the grid and to provide these standards to "fool" the inverters into switching back on, but at the power level you're talking about it would not be an insignificant expense in engineering and hardware. Grid intertied solar systems are really not meant to be used for standalone power; they were developed to "cheaply" offset site grid energy costs using the local site and/or grid as their "load." To try to convert one into an off-grid source means you will be fighting the entire design concept implemented.