I really think they need to team up and kill the current king. That's who ordered Heeryang to kill Yeonjoo's family. Ultimately, the king is the one Yeonjoo should get revenge against, he's the usurper and the actual traitor. The king was the judge and Heeryang was just the executioner. Let them get justice for Yeonjoo's falsely accused family. It's the only way Yeonjoo can move forward from his feelings of grief and his guilt for loving Heeryang. It's also the only way for Heeryang to redeem himself and be even a little worthy of that love. Heeryang gained his government position by harming Yeonjoo. If he claims to love him, then he needs to be willing to sacrifice that position to help him. Otherwise there is no character growth and this whole story just becomes pretty pointless and cruel.
I really think they need to team up and kill the current king. That's who ordered Heeryang to kill Yeonjoo's family. Ultimately, the king is the one Yeonjoo should get revenge against, he's the usurper and the actual traitor. The king was the judge and Heeryang was just the executioner. Let them get justice for Yeonjoo's falsely accused family. It's the only way Yeonjoo can move forward from his feelings of grief and his guilt for loving Heeryang. It's also the only way for Heeryang to redeem himself and be even a little worthy of that love. Heeryang gained his government position by harming Yeonjoo. If he claims to love him, then he needs to be willing to sacrifice that position to help him. Otherwise there is no character growth and this whole story just becomes pretty pointless and cruel.