[X] You will have your younger brother become the Lion Champion with Akodo Shigetoshi and Matsu Yoshino as regents until he is of age. This is a rather drastic step, but none can really deny his claim. Although you will have to betroth him young if you do that.
[X] Simply appoint Akodo Shigetoshi and be done with it. Make some political appointments to salvage the Matsu's pride, and hope enough of them die in the oncoming war for it not to be a problem.
[X] Unite the two lines with Akodo Dairuko and Matsu Yoshino. Akodo Shigetoshi will remain regent until Yoshino is ready to take over. No one will be truly happy about this. But the Matsu are unlikely to complain over much outside of Matsu Yoshino's direct family.
[X] Arrange a competition between Akodo Shigetoshi and Matsu Yoshino in the upcoming war. Both will be granted an Imperial Legion to use, whoever does better in the war as determined by your Shogun will receive the Championship