Perhaps it's been mentioned, but I suspect LE and the FBI know who Jayme's with - they just don't know where she is.
If they have the perp's description and/or identity and he is alive they will eventually find him (and Jayme, if she is still alive and in his possession). If LE is under even the remote assumption that she is alive, they will bide their time until he is located and close in on him silently.
They won't publicly disclose the perp's description or identity because it wouldn't do Jayme any favors; rather, it would tip the perp off with the knowledge that if LE had managed to obtain his identity it would indicate his capture would be imminent. The disclosure of that information and the perp's knowledge of it would, of course, increase Jayme's risk of meeting an unhappy ending.
IMO, unless some clue pops up as to her whereabouts, I don't think there's much here that anyone can do other than speculate who took her and if LE already knows the perp's identity then it would be pointless. It is also unlikely that LE would publicly release his identity unless they find Jayme deceased, making futher speculation about the evidence they removed from the home also pointless (they won't release information they gathered from that, either). It goes without mentioning that if the perp reads forums that could turn things into a double-edged sword. My guess though is that he's keeping an eye on MSM for newly-released information. Would he dare the use of a mobile device to browse the web? I think not....definitely not his own, and not unless he wanted to risk sauntering into a Walmart and paying cash for a Tracfone. The dude does seem brazen enough to do it, and if he's as reliant on the Internet and social media as most people, he might think a baseball cap, stubby facial hair and frumpy shoes would suffice as a disguise.
Having said that, I'll leave it to the mods to decide whether my suspicions have any merit (I was very ambivalent about posting, but how else to get my message across?), and if so, whether to remove my post or even allow the discussion to continue....it might do more harm than good.
I'm just so worried for Jayme, and am concerned that with aggressive sleuthing, close-to-accurate details might become too public, hit too close to home with the perp and bring harm to Jayme and the investigation. There is a chance she's alive.