Yihwa is an average tsundere, and damsel in distress. If TOG was boring jap isekai this would work, but TOG is much more than that. Yihwa can be a good friend, but as love interest, it would be boring. Kaiser is too undeveloped for this role too, also she was out of practise for a long time, and considering Baams goals and road that he took, I can't see how this would work, except physical terms of relationship, aka simple sex. Rachel, it's just no, please no, it's as bad as yaoi with Khun which I hate. Hwa Ryun is possible, but FOR ME, it's more like religious person worshipping a god, rather something physical. Also she is too moody for Baam. Androssi, I know why people like her, she is female fatale. I have same problem with Batman, where everyone love catwhamun and love batcat pairing, which I can't stand. Same for Androssi, and situation worsened after Name hunt station. She is self obsessed prick, situation turned for better before Last Station battle, but yet, the damage from Name Hunt station, would never let me, if I have had ever considered Androssi as love interest for Baam, is too big damage for her and her relationship with Baam for my testes, to give me reason to pair them together. Eurasia is sealed, and we don't know her situation, aka she can be batshitcraze. Also there is important part for me, is her connection to Baam, the gals above have at least have long history with Baam wit one way or another, which can't be said about Enne, and next candidate Adori. In terms of pure strength she is good pair for Baam, but she is Zahard army supreme commander, she is psychopath too, also, as said above, she had no connection to Baam, there is no attachment. Then goes Yuri, she have all qualities above and combined to be with Baam, strength, influence, connection, attachment also which is more important, same goals. The story for Baam in the tower started with her and it would be logical that it would ended with her too. She is the hope embodiment for Baam, she literally put her life under danger of death and her head under guillotine just for him, to help him and guide him. I will not accepted anyone else next to Baam(as love interest), than Yuri Ha.
p.s harem root is impossible for Baam, if he is repeating Zahs story, and he is Zah but better, then as Zah he would have one and only love, and would be devoted for those feelings and that woman, till the end. I don't see him as someone like Eduan Khun. It's out of his personality and life-view.