The situation after Sons of Mogh really wasn't any different for Kurn than the situation after Sins of the Father. Just his brother was the traitor instead of his father. And Kurn knows how politically unstable Kronos is better than anyone, he knows just because his house is dishonored now doesn't mean it will always be dishonored. All he had to do was bide his time until he had something of value to offer to a political leader, the exact same way he did in Redemption.
There is a difference here... in SOTF Worf told Kurn to hide his identity in case things went bad, which they did. Duras did figure out who Kurn was, but they were never clear on whether or not word got our to everyone.
By the time SOM rolls around, Kurn has been living it up in Gowron's good graces as Worf's brother. So I tend to think Gowron's rather harsh reaction towards Kurn is probably his way of further punishing Worf for publically going against him.
Though I do agree with what you said at the end. All Kurn needed to do was lay low and bide his time, he knows how volatile Klingon politics can be.
And what about his family? Worf once mentioned Kurn's children to Alexander back on TNG, what happened to them?