Why not just run the generator on its own instead of coming up with a dump load system and potentially running an unloaded generator? An unloaded gas engine is an inefficient engine. Gas generators with an alternator directly producing power will likely not be clean enough of a power source to where the inverter will want to feed power. How would you plan to run this dump load, inverter, and generator to synchronize the loads, sounds like a PITA.
Why not just get a grid tied system with an inverter that is designed to produce its own sine when the grid is down like the Sunny Boy with the built-in Secure Power Supply?
SUNNY BOY 3000TL-US / 3800TL-US / 4000TL-US / 5000TL-US / 6000TL-US / 7000TL-US / 7700TL-US
That sort of solution would remove the need for a crazy solution like a generator. If you want to be sure it works without sunlight or running loads beyond the possibility allowed by the level of insolation provided at the time, you could get a small battery-backup type grid-tied system.
Think of your mission with doing this. Do you frequently have power outages that warrant the extra expense of batteries versus just running an appropriately sized generator for the loads needed in an outage? If you have a generator already and don't need individual MPPT on your solar system and a string inverter 3-7.7kw works for your application, the SMA-America Sunny Boy can provide you with a 1.5kw power source if enough sun is present to provide for your load without raising the cost of your solar system by much. In that case you can use your generator at night and pull power off PV during the day.
I considered this system but I have a partial shading issue and also really like the production I got this winter with a partial snow covered array with individual MPPT versus nil from a single MPPT string. I'm quite certain I'll produce more than I'll ever spend on gas for the generator in the edge case that I ever need it. Oddly my generator has only supported a load once in the 5 years I've had it and it hasn't even had a full tank run through it. Think critically about how often you'll need a generator when making the decision for a complicated weird dump load setup thing.