The breaker is mainly intended as a disconnect for times of service. Class t fuses protect everything, but still it seems possible if a cheap breaker were to fry it might take out the inverter. @Skypower that makes me feel a little better about this breaker. Thanks for that informative post.
Manual recommends 8gauge, and honestly, it was hard enough to get 8 in there. I'd feel better with 6gauge but not sure 6gauge would fit in the box and insert securely into the spring loaded lugs. If 6gauge did fit, it would definitely be a struggle. My fingers are all cut up trying to fit 8gauge wire into that tiny space. A larger lower wiring box would be a huge plus.
I didn't find much when looking for a 300amp breaker. Your search ability is better than mine.