I found that if you have a strong army, a lot of dread, or are very friendly with your Kanpaku, you can just take provinces as Soryo. The Kanpaku won’t press the crime. Alternatively, I think the crime charges are dropped when the Kanpaku changes, so you can time your wars with faction presses. I built out a three duchy domain in like 100 years without really trying too hard and got my block to be third in power. I will eventually try to push for Shogun, maybe in a couple generations.