So it stands to reason, that going solo and taking that power away from them, will grant/return it to Eva/Cam.
How?
The only possible way it would benefit them is if the queen was constantly in the public eye, she isn't which means the public has no way of knowing what's going on which also means the priestess still controls the narrative.
The priestess also still controls access and going solo means the warriors won't back up any play Cam makes. He's literally on his own in hostile territory with no way to leave because they also still control the only way to repair the ship.
Even if the queen ordered repairs they only need to get it to take off. Leave a few breaches here and there and atmosphere takes care of the rest.
Erylin is also a political snake that's been planning this for some time, if you think for 1 second she's suddenly going to play nice because you killed a bug and a bit of public praise I think you may be in for a shock.
I don't understand why some people think just because he won the hunt that 2 factions vying for control of their planet are just suddenly going to stop and bow to his whim..... You are in the way of both of their plans, they aren't just suddenly going to stop those plans because you say so. Even with winning the hunt do you honestly think the people would allow him to take their queen?
Like I said, you may get the respect of the people but that will only go so far only now you have no friends at all.
I hope it goes all sunshine and rainbows for you but I very highly doubt it will.
Now, if I was the priestess i'd give him all the access he wants, i'd even leave it open for him to make his escape. Then i'd spin the narrative he'd tried to kidnap the queen and take her away from her people which not only takes away any good will he won from the hunt but also puts him and his crew at my mercy. The warriors wouldn't help, his crew are outgunned.
I'm just glad i'm not on your crew. You risked pissing off both factions and pushing them into a corner hard enough for them to have to fight back on the hope things will turn out okay. Basically you risked the lives of your entire crew on hopes and wishes.
In a game that's already shown mass murder, torture, kidnapping, murder and a woman okay with killing her own children yet i'm seeing people think not picking sides will make everyone friends ..... amongst a people on the verge of civil war ..... with one of those people being a power hungry narcissist willing to offer up her own daughter against her will just to get him on side.
I don't share your optimism.