After retrieving the madstone, and following through this incredibly interesting quest, the countess doesn't believe I have it. I'm using the pc version, so I'm willing to do anything to get around this.

OK, after trying a bunch of different console commands, I have discovered that I am stuck at stage ms12 110, and for some reason she won't accept that I do in fact have a madstone. I made sure of it because I added a second madstone, and a second version of a madstone (this one you can wear)

So, I set the quest: MS12 to stage 150. I assumed that my logbook would be inaccurate and the game wouldn't act as if I've completed the quest, but beside her display case magically appeared the correct quest items, my logbook updated, and I can now purchase a house in Bruma!

It's quite an annoying glitch, but this fix changes absolutely nothing in how you would normally progress. The only thing I missed out on was the comment she gives to the player for completing the quest, and the reward she gives to the player. I guess I'll need to use the console again to acquire whatever it is. The uesp was incredibly helpful, but it looks like I found a new bug.

Did you by chance complete the Defense of Bruma quest somewhere in there? If so, that can sometimes cause the Countess' dialogue regarding the Madstone quest to not work correctly. Aside from that and, given the age of the game, I would be surprised if what you describe is a 'new bug'. Generally when such undocumented oddities occur at this point the answer is most often mod interferance. I'm not sure if you are running mods or if, indeed, that is the problem, but it often turns out to be so in such cases. Regardless, I'm glad you were able to get it sorted ok!

Yes, I completed the main quest, but it's strange that I can speak to her about it, but she claims that I don't have it in my possession, even though I clearly do, and my logbook agrees. Oh well.