Three theories?! I only have half of one theory, and I don't have much confidence in it! Coming up with two and a half more has my brain in a snarl of questions, contradictions and doubt - usually a good reason to keep ones mouth shut. Nevertheless:
-- JT, a bipolar, is thrown off kilter by some unidentified stresser in his life and cycles into a hyper-manic state in which judgement suffers and confidence abounds. His already difficult relationship with Julia hit a crisis for some unknown reason and he jumps to the conclusion that a brilliant solution would be to kill her. He's been to her apartment before, and knows, from family members who visited her on the day before her death, that she should be at her apartment that evening. She lets him in the door. He uses a choke hold, which he was able to master using his martial arts skills, to kill her without leaving outward marks. He tries to wash fiber or DNA evidence off of her in her tub. Whatever DNA evidence he does leave has to be written off by LE as explainable thru JT's and JN's known contacts. JT is able to provide a fake but plausible alibi.
-- An acquaintance of Julia's visits her, freaks out for some unknown reason, chokes her in a way that, by sheer luck, leaves no marks. The killer moves her body to the bathroom with the vague thought that it would be less likely to be seen thru the curtained first floor window in her room. The killer is a man (strength and violence) with problems with impulse and anger control. He is familiar with Peninsular Place and might already have been in to her apartment for some legitimate reason. Wierd bad luck somehow prevents LE from quickly scooping up a suspect for this unplanned, amateur murder by someone with links to Julia.
-- A serial killer with great charm and or conning skills talks his way into an acquaintance with Julia and gets into her apartment with her permission. He artfully asphyxiates her. He loses his mojo, or didn't have a sexual motivation in the first place, washes the body of trace evidence, and leaves. (I think that TSR* should be alerted to this theory).
I'm going to go back now, if I may, to the maps, where I have more of a chance of being right about something.
* TSR = Television Script Writers.