Himiko, if you are aware of the dirty trick the influential people employs to gain control over others by making them indebted to them, then maybe you should've planned further and did some compromise so that you and your fleet doesn't got put into a position/situation where you basically have only two choices; complete annihilation or accept Beiyang's help and then being ever greatly indebted to them. Prior to the Cloud Immortal Planet Conquest, Mu Siyun and Beiyang had offered assistance. You feel you'll be indebted to Beiyang sure, but let's be honest, having a "you assisted me on an important mission" debt is a mile friendlier to one's consciousness than "you helped me and my entire fleet and saved us all from total destruction" debt, lol.
I do have a feeling that maybe ever since Ditu had his hand on Three-Legged Crow, Himiko is basically got a little traumatized and now paranoid to any instance of her and her fleet being in debt to someone's powerful. Topped with her passive-submissive personality previously, this maybe was the underlying reason for why she's really against accepting Beiyang's help for this Conquest mission.
Regardless, in the end Himiko, you kinda set yourself up (to be Mu Siyun's Mistress) here. XD