Thanks for the detailed report, it helped a lot! You found a real bug: the objective only counted a ransom paid after "Past Dante" started, and rival raids were purely random, so you could wait forever.
It's fixed in the next update: while "Past Dante" is waiting, Dante will raid one of your cages within a couple of days. When that happens you'll get his letter in your Mail; pay the ransom from there (you need the money and a free cage), and the objective completes. Buying the person back at Idris' counter in the Undercroft also counts.
Your current save will work too: the ransom you already paid will count as soon as time moves forward after you update, so no need to start over.