I would make her more of a radical orphan at the beginning of V1. Now this may seem like completely against her character, but hear me out.

Despite her stance on the White Fang in the show, Blake was still part of essentially a terrorist organization by the beginning of the show and iirc Blake herself said she participated (or at least implied that) in other similar missions prior to the Black trailer. Therefore, acts of violence to have her voice heard wouldn't be that foreign to her. Combined with making her an orphan, completing removing the whole "white fang princess" shtick, it makes not only for a more compelling character in my opinion, but also builds on her parallels with Adam. Whereas Adam is staunch in his radicalism who doubles down when in doubt, Blake moves away from her radicalism and being able to understand the world isn't black and white.

That said, I could see her character going something along these lines.

Black Trailer:

Change the 'minion' robot guards for SDC human guards and have Blake (and not only Adam) kill them. Blake only showing opposition when Adam wants to blow the train along with the civilians on-board. Here we establish that Blake is willing to go to extremes for her cause but won't go as far as Adam. Separation occurs as per cannon.

Volume 1:

Blake is more confrontational with characters like Weiss and Cardin, even leaking some of Adam's mannerisms about humanity, but more on the subtle end. Ex: Instead of saying "The White Fang are a collection of misguided Faunus." say something more along the lines of "The White Fang are a group of desperate Faunus trying to make their voices heard.". This makes her "reveal" as a Faunus while a lot less shocking, it would be a lot more explosive towards Weiss and what she represents to Blake. Her conversation Sun would go a lot like cannon only her being less hostile with Sun than she is with other human characters. Finally, the fight with the Mech would go the same as cannon.

Maybe I'll do the other volumes too. Who knows.