Powering off the phones by removing the batteries shows an abduction, likely outside the home, by a non-neophyte assailant (i..e., not a crime of passion). It could be possible to search the home, find all phones, remove their batteries, and bring them with an abduction victim but I wouldn't put much odds on it.
It is what an assailant would do when abducting a victim in their car and driving off in it. It is critical to completely disable (i.e. not accidentally put in something like sleep mode) all cell phones in the car. At least circa 2006. I imagine it is much more difficult to keep a car from being tracked circa 2016.
In 2006, my assumption is that "battery removal" indicates that a phone fell on the ground (or what not) and the battery became loose. Jen was known to call someone on her phone if in a situation where she felt vulnerable, so if she were attacked before she could make such a phone call, it strikes me as a logical scenario. Of course, it would be worthwhile to know exact data for both phones.
Blink maintains (at last check) that the ping data specifically suggests that the battery was removed from Jen's phone (no mention of the other phone's pings). Not too long ago I looked online for feedback regarding whether a phone could ping a cell tower while powered off. Basically, it seems that at least some phones will ping a tower when powered off - I found this stated elsewhere on WS amongst sources. However, the signal from a cellular tower needs to be a certain strength for a powered off phone to ping a tower. I mean the end consensus is that nobody really seems to know this stuff, but at worst these assumptions do not appear to be contradicted easily.
No phone will ping if the battery has been removed or is completely dead, but phones tend to power down automatically before the battery is completely dead. So it seems hypothetically possible that ping data would reveal that a phone's battery had been removed.
In any event, even if both phones were simply powered off, it would appear that Jen never turned her phone back on in the morning. Not to mention, on Monday night Jen is presumably exhausted, she had what we are led to believe was a minor argument with her boyfriend, there are various hypothetical reasons she may have decided to leave her apartment, ranging from a trip to the drug store to who knows what. On Monday night she is presumably in a much more vulnerable state than on Tuesday morning, which puts her at greater risk of abduction then. A predator is also, presumably, more likely to strike at night as opposed to broad daylight (and more people out and about).
Monday night IMO is a more logical time for her to have crossed paths with an abductor, than Tuesday morning. If LE says otherwise, I question whether they are simply taking steps to avoid contradicting Jen's parents in order to avoid discord and guard against negative publicity.
The wet towel was, I believe, found on top of her drying machine and could have been taken out of the washing machine the night before. The wet shower, I'm not sure for the explanation but it feels like there could be one. All items missing were items she would have left the house with for work; either she kept these things in her car for convenience, or she was planning to spend the night somewhere else. I can't really get past the cell phone data, though.
Were there calls / text between jen and MS ? If there was to be a handoff of a phone at blue martini I'd think she would verify vs out randomly driving around, even if he was a frequent patron of the establishment.
I tend to doubt that she would have bothered bringing the phone to MS unless she had other motivations. But if she was angrier than we are led on after getting off the phone with her bf, I tend to wonder if there was anyone she might have turned to. I presume that there were no phone calls to anyone but I wonder if there would have been electronic record of any instant message sort of communications, i.e. by computer or old school "app." I also wonder whether anybody ever looked for such communication.