I agree with your second paragraph. I don't think he subdued her at the park, he certainly did not kill her there in that short of a time period. I guess he could have disabled her but I doubt that as well. I think she went willingly all of the way into his house, which was his goal, getting her home for whatever the sick and twisted plan was. Into his house, in his head no provable record of her seen with him or going there--into his house under his total control. Could she have had a clue by then? Possibly. For all of his stupidity with an in town fire later, etc., I think this first part he had planned. He thought he was covered, no airport cameras, the park, not his address, he was not seen apparently--Lyft driver did not know if female or male(?). I don't see him at his home 7 or 8 minutes later, carrying her in or being seen trying to move a body or incapacitated woman into his house or yard... I also do not think the texts are going to show such a plan as meeting at the park, IF they have the texts, they have proof of contact but the actual texts I am not so sure of (based on something said awhile back in a PC). He thought he was covered up until that point (in his mind) and could just say he talked with her online but never met her...
To each their own, but your IHOP paragraph, I differ on (respectfully). I do not believe this was a "go to breakfast" meet me at the park scenario. You meet at IHOP, not some out of the way park, even allowing for naivete on her part, why not save the bucks on the Lyft and meet at the IHOP instead of some out of the way park? I think from that direction they have to double back to even get to? I do not believe they were meeting at the park to go to the International House of Pancakes...
Jmo though