Connecting varaible DC to PV input of Solar MPPT inverter
This project of yours may work, but I highly doubt that it will fulfill your expectations.

Here's why:

Solar PV inverter will search for MPPT, and, assume the source has a V-I curve of a solar panel. Now, your generators VI graph and MPPT point is much different than that. Because of that, the inverter will never catch the MPPT. Its output will fluctuate. So if there is an option to shut off MPPT, please do so.

Secondly, how will you rectify 4kW of AC power to DC? Just using diodes and capacitors? You'll need huge capacitors and the level of harmonics in the DC side will probably cause the solar inverter to go insane. The inverter probably will have a modulated output.

I think you'll be better of with a pure sine inverter and batteries instead of capacitors.