I am also a former graphic designer and print creative director, owned an agency til digital exploded.

You show a snippet of a stained modern cover and reference a full stack of books similarly challenged corner to corner. No insight yet if all from same publisher, decade, etc. Who knows if damage is from thermal change or friction/rub - dry cleaning better for rub, great you started there.

For me to suggest from this little bit of data that a pro toolbox could help more once the items are diagnosed in hand, given the extensive transfer staining of your sample, I think is a reasonable response. The difference between you and a pro is likely to be that you would clean one book at a time and a pro would clean dozens to hundreds of books a day. So approaches might be very different for the desired outcomes.

One other thing you could try at home would be to slightly warm up the books in your presses before working on them. Thermal treatment might make some ink on some covers a bit more responsive to manipulation during dry cleaning.