Its difficult to 1-HKO with Kinjo and Lost Hog. But if you insist on going that route, then I would stick to one or the other. Having two takes up a lot of stars.
As an alternative, you can add Timber and try to get as many 7 damage cards -- Tsubame, Zinfrid, Ryuichi, Sung Tsu... You won't be able to get them ALL in the deck, but you will be able to get your 1-HKO a lot easier.
When I did the Lost Hog and Kinjo missions, I used them along with Chan, Fei/Zinrid, Windy Mor, Yumi, Nakata, Kati, and Unagi.
Sometimes I subsituted Unago and the Kati or Fei spot with Rei and Sayura -- during times that I saw SOA wasn't used much.
I all things fail, there is always T2. 