Good points. A few thoughts:
The neighbor may not have had the opportunity to ask Tim why -- Tim may have called across the way to the neighbor and then gone inside, or may have otherwise nonverbally communicated that he didn't want to talk, even if on some level he did want to talk. Or maybe he would've felt more comfortable talking with the wife but happened to see the husband.
Also, even though I tend to think this was a cry for help, another possibility has occurred to me. I'm wondering whether the number in the neighbor lady's phone was to Tim's personal phone or his work cell phone (or possibly to a work office number, though I doubt it). (I think articles have implied he had two cell phones.)
Could Tim have thought he was in trouble for receiving too many calls at work or to his work cell phone? Maybe the woman next door tended to call with messages such as "Bo's barking again."
They said they found everything that belonged to Tim -- I'm guessing that included his work cell phone, if he had one. Though if he'd lost the phone, that might've been another reason to tell people to take its number out of their phones.
I'm still inclined toward the "another cry for help" theory, but these are some other possibilities.
I'm sure his mother is upset that she didn't pick up on that early morning text or later call. I'm sure if she'd known what was going to happen, she'd've kept her phone on. As you say, he either had had other instances of drama, or on the other hand, maybe drama from him was so unusual that she didn't think answering every call would be important.