Some inverter/chargers, especially utility interactive ones, require incoming AC to be within grid specs.
Sunny Island has different voltage/frequency range for generator vs. grid.
It can also be programmed to limit current draw from AC to whatever you want, e.g. 56A max, 10A, etc. so small generator should be OK.
See if you can just open up specs, maybe reduce draw.
Can you just have the Generac power a battery charger? As little as 1kW should meet your needs, but try to use Generac at its most efficient loading.
Other hacks could include rectifying Generac output (perhaps after boosting to a higher voltage if needed, and transformer-isolating from ground), and feeding DC rail of Sol-Ark (e.g. treating rectified generator output as if it was a PV source.) You are on your own doing that! could cause damage.
Feeding Generac into a GT PV inverter, AC coupled to Sol-Ark. There are wind and solar inverters; this would be similar.