I had a thought: I wonder why it never occured to Rover that if they disapproved of Phrolova's choice of employer so much...Why not just poach her from them? She's a living, walking Lament remnant, so she'd have massive value as research material (as dehumanizing as that is to say but it is what it is) AND, quid pro quo, she'd have access to the Black Shores' massive library of Lament research that she likely didn't have access to before. They could make some real breakthroughs together AND it keeps her from siccing TD invasions on cities on orders from the Architect. Yeah, I know Phrolova said she tried the science angle before and got exploited for it, but this is the Black Shores, headed by best girl Shokie and Rover, they'd keep things on the up and up.
Bonus points, Phrolova might actually get that conversation she was denied hundreds of years ago or at least some context about why Rover flaked. Closure helps a lot sometimes, I dunno.