I'm noodling on a plausible explanation for a crib on the 26th, but no crib at the Homegate, if indeed there was no crib there.
Sex on the 26th would a plausible explanation.
Here's the thing. LE has had all this info, and more, longer than we have, and yet they have opened a homicide investigation. That tells me there is likely a plausible explanation for all this that doesn't include Elizabeth giving Gabe to someone/a couple.
But yet, we have her and HG and the couple in the parking lot. So how to explain all this, where the HG and the couple are uninvolved in anything with Gabe, and then combine that with all this info we have.
What I've come up with is a scenario in which HG arranged a sexual encounter for $$ - or to try something new - between EJ and the couple. They would not want to deal with Gabe while doing their thing. So I've got HG with Gabe in the travel crib at the Quality Inn, and EJ and the couple over at Homegate.
It accounts for the unusual act of paying for 2 hotel rooms for the same night, and gives a simple, not-too-extreme explanation for EJ, HG, and the couple where HG and the couple aren't involved in taking Gabe.
But... I can't lose the feeling that HG and the couple are involved in taking Gabe.