Sometimes, I just Forrest Gump my way through missions, but this is how it seemed to fix itself for me:
I abandoned Blood on the Ice very long ago, having gotten some steps I simply couldn't manifest during the Investigate the Crime Scene task. Just....nothing to see.
I went ahead and completed the Imperial side of the Reunification of Skyrim quest, bought Hjerim, and walked in. There was my housecarl sitting in a desolate house, but the Steward wouldn't sell me upgrades or decorations. No menu at all. I hadn't looked hard at the house (even after getting the task to do so. I was just put off by this mission.) I was stuck. I searched the house, and found everything....Butcher journal 2, strange amulet, flyers, etc. My original Butcher journal had glitched in a Lakeview Manor bookcase, so I figured the quest was screwed. I also could not locate Viola, despite having seen and spoken with her about another Miscellaneous quest quite recently.
So I came here to see what little help might be offered to a 360 user who can't do console commands. Someone suggesting looking for Viola's coffin in the Hall of the Dead. I Gumped my way there, looking for Candlehearth, and counted myself lucky. THERE was that NPC I couldn't find...the mortician examining the body. This completed a stuck task. I assume that 'Investigate the Crime Scene' and 'Follow Up on the Clues' are multi-task missions which require talking to some NPCs more than once. After talking to the mortician, forr some reason, this permitted Viola to start appearing in Candlehearth again. I spoke to her, and the mission was back on track. Once I spoke to the Steward, the Court Wizard was arrested and jailed.
Note, nothing occurred to progress me until I followed the guard escorting the court wizard all the way down to his jail cell, where all of his normal menu vanished except offering to train in Destruction. After that, I spoke to the Steward, and he offered the upgrades and clean-up option.
So, having done so many things so far out of order, I'm amazed the mission cleared, but it has, and Hjerim is now habitable.
I have no idea if this will help anyone, because Blood on the Ice was the most frustrating mission of all, particularly when it kept me so long out of such a cool house.