Don, I have to on one hand understand why the investigators did what they did (if not *how* they did it..).. but on the other, I am so sorry you and Jill had to go through something so horrific, on top of all the other things you must have been feeling at the time. I'm 'hearing' some of that distress in your words, even after all this time.
Have you ever speculated on your suspect's motive? If so, would you talk to us about that? He must have targetted Jane for a reason..?
If he was a lust killer there'd likely be other assaults at least, possibly other deaths. Women around him would have stories...
If it was a one-off crime that was aimed at Jane alone and never anyone else, he had to have a powerful motive regarding Jane in particular on the night he killed her. Maybe not an obvious one. But he would have had one. Perhaps a motive that had been festering for a time, if he indeed snuck up the fire escape rather than just barging up to her door...
He must have attacked Jane quickly and she could not have seen it coming. No screams were heard, and you and your wife were so close, right next door, and I dare say those apts were far from sound proof. Plus, Jane (from all I have seen of her) was a fit, strong-minded, fiesty young woman. I cannot see her at all meekly standing by if somebody gave her any chance to fight.
I seriously doubt the situation began calmly and then escalated. Somebody would have heard it.
This was, for all I can see, a rapid and silent attack. Possibly, with a weapon brought to the scene. That suggests to me: premeditation. He set out from his home that night to kill Jane and nobody else.
So he must have had a strong and very personal motive, if he was someone she knew. And because it does not look at all to me like a simple, drunk and blundery crime of passion-in-the-moment, he perhaps had a 'dark side' to him that had manifested elsewhere in some way or other.
He might be the type of guy who never did take refusals or opposition well, on any level. Prone to bouts of rage, or dead-eye creepy and then he'd get even - and boast about it.
I just cannot see an average joe (who might be a nice guy, otherwise, except this once he lost control etc) sneaking up on a girl in her home and caving her head in with a blunt object, and not making a sound, nor leaving a blazing trail of evidence.