I have not considered Morse a viable suspect due to his alibis, but he does have the distinction of being the only other non-resident person known to be present in the home close to before and close to after the murders. Bowen is next in line.
I've always entertained the idea that Lizzie brought the killer into the house under cover of darkness after leaving Alice's the night before. The best place to hide in No. 92 without fear of being found by anyone would've been Emma's alcove. This entirely eliminates the issue of how the killer got into the house unseen on the morning of the murders and the issue of locked doors. Escape via the basement door with Lizzie relocking it, a dash across the backyard, a leap over the fence and he's long gone before Lizzie sounds the alarm.
I do think Lizzie killed Abby - the overkill fueled by rage is not something one would expect from a hired killer or even someone connected to the household who merely held a grudge. This was Abby, not Andrew; she was not the one who made enemies both personally and professionally...except for her step-daughters. Either Lizzie killed Abby, or Emma somehow did.
However, Lizzie tells us that her father will be killed by a man who holds a grudge against him. And that she fears the house will burn down around them.
Alice's testimony:
A. She said, "I feel as if I wanted to sleep with my eyes half open—with one eye open half the time—-for fear they will burn the house down over us."
Q. Is there anything else that occurs to you in the conversation? A. Oh, she said, "I am afraid somebody will do something; I don't know but what somebody will do something." I think that was the beginning.
Q. Please state that.
A. "I think sometimes—I am afraid sometimes that somebody will do something to him; he is so discourteous to people."
I like MB's theory that Lizzie was in the yard as seen by Lubinsky for the purpose of being seen while her father was being dispatched. She could kill Abby, but couldn't bear to present at the death of her father.
The reason I don't see Morse as the killer is he looks more like the spoiler. He arrived unexpectedly and was invited home for lunch. (I'm unsure when Lizzie learned this.) This forced Lizzie's hand and the hand of her father's murderer. They couldn't wait for Morse to arrive home, go up to his room and find Abby dead with Andrew still living. They couldn't get Bridget out of the house (someone reported she was the best dressed member of the household, so a fabric sale should've been adequate bait....)
As Curryong mentioned in the other thread, Lizzie made her first and only attempt at luring Bridget out of the house to a fabric sale mid-morning on the day of the murders. Lizzie intended to prevent anyone from searching for Abby by stating Abby had received a note to visit a sick friend. No one would find this unusual, especially if Abby's burned corpse sans the incinerated note was discovered once the house had burned down around her and Andrew's bodies. Write it off to Abby arriving home early and walking in on the murderer, fleeing upstairs and being cornered in the guest room. Arson has covered up plenty of murders or at least misdirected attention away from household members who were out shopping for fabric or fishing line. A misquided attempt to hide her body under the bed supports this theory.
Remember, Lizzie paid an unusual amount of attention to that kitchen stove on a hot day in August (yes, I know, not the hottest day but rather a Thursday - Bridget's afternoon off) for the simple purpose of ironing handkerchiefs. I'm more inclined to think Lizzie wanted the fire kept capable of being overfired and engulfing the kitchen followed by the house. This might be why she hid her dress next the stove...it was supposed to be among the first items to go up in smoke. (With apologies to Cheech and Chong.)
The hatchet came into the house with the murderer and left with the murderer. Maybe it went home, got cleaned and chopped kindling for many more years. Maybe it was tossed in the bay. I do not think it was tossed onto Crowe's roof. Once the killer made it over the fence with the murder weapon, disposal opportunities became far more global....

Lizzie had plenty of time to kill Abby, clean up and write it off to a bloody slops pail in the basement. (I will always wonder if Lizzie said something to Abby like, "Those windows are positively filthy, aren't they Mrs. Borden," which got Bridget sent directly to wash them...exactly where Lizzie wanted her.)
We've discussed how a conspiracy could not have lasted until the death of those involved; someone, sometime, would've been in the throes of love, lust or liquor and spilled the beans. I do believe this is an element needing careful consideration, and that success would depend entirely on the characters of the two individuals. I'm more inclined to think this kind of loyalty cannot be bought but rather arises from love and deep friendship plus a common motive. Note that Lizzie does not say her father is in danger from someone he has cheated; instead she says he is in danger due to discourtesy! Given Lizzie's semantic issue with the definition of cordial, I'm inclined to think 'discourtesy' is exactly what she meant.
If each of them killed one person then each of them held the power of life imprisonment or death over the other. Even Lizzie's acquittal in the deaths of Abby and Andrew would not prevent her from being tried for conspiracy or obstruction of justice regarding her partner...perhaps not hanging offenses but life in prison is a far cry from life in Maplecroft. This makes me wonder whether Lizzie's version of David Anthony was somewhat true but totally self-serving.
I am convinced that Lizzie slipped the coat under Andrew's head as a means of undoing. His injuries indicate depersonalization so the killer was likely someone who had amicable dealings with him in the past and then became infuriated. The coat was not in the ideal place to disguise blood splatter...to do that it should've been directly under his head not several layers below. I also think Lizzie is telling the truth about making him comfortable, tending to his needs when he got home. She wanted their final interaction to be loving...before he was hacked to death.
Regardless of all else, I have come to believe that Lizzie was telling us her game plan which included burning down the house and all the evidence inside it.