You really don't want the generator to "top off" your batteries. That's really a waste of fuel. You'll get the best performance if you start the generator in the very early morning, and bulk charge past 80%. Then shut the generator down and let whatever solar resource you have finish the topping off.
What your inverter might do is want to "qualify" the power coming in from the generator. That means the inverter looks at the voltage and Hz stability and decides whether or not the generator is "qualified" to supply power to it. In real-world practice, I've found that as you inch the charging rate up, it becomes harder and harder to get the generator "qualified". That is, the inverter will accept the power at a lower charging level, but reject it if the generator is getting too labored.
I'd recommend going with a generator at least twice the capacity you want to charge at, so the generator is not being pushed so hard that quality drops. You should go into your inverter's menu and find where the charging setting are and play with them.
Inverter generators are supposed to have a cleaner sine-wave, so that most likely will help with the qualification process.