Even with all of his lies, that won't be enough, Imo, to charge him. They need to be able to show that Christina came to harm at the hands of EA. Blood in his vehicle or clothing linked to her would be a good start. Casual signs of her being in his car may not be enough either. I say this because I have heard detectives in other cases marvel at how many people lie to police, about stupid things even when innocent, and about things that can be proved a lie, and will not admit their lies until shown proof.
I am not saying other pieces of info don't add suspicion (injuries, lateness to work, etc) but from what we have seen so far, it is circumstantial evidence. Which is fine, if it all paints a picture that can lead to no other conclusion. If they had that much though, I think he would be charged with abduction, as was Hannah's suspect, who has yet to be charged with her murder (which is odd to me...they feel they can show JM abducted Hannah with evil intent, yet no added charges for murder at this time.)
How LE can tell who sent a text is baffling to me.
All JMO