That he drove the van back home to FL indicates that he considered it his van as well has hers, a shared vehicle that they lived in together, and he mostly drove. (Remember, she said in the bodycam #1 that she didn't drive it that much.)
Even though the van was in her name, it seems that they considered it their shared vehicle. Coincidentally, the Mustang in FL is apparently not in his name either, but seems to have been what he drove. His driving the van home to FL indicates to me that he considered it his as well as GL's van, and it was his only form of transportation, in his thinking. If he were thinking more strategically after killing someone, it might have been smarter to leave the van at the scene of the crime and get his parents to buy him a ticket home with a story that he needs time away or they broke up or whatever.
Returning to FL in the van without GL indicates to me that he [allegedly] knew she was dead. I believe he loved her/ they loved each other (based on the length of relationship and their plans to get married). You don't leave your loved one behind, thousands of miles behind, without the home (van home) they were living in. You don't go home and then just carry on as if everything is normal. That indicates to me that there was no GL to bring back, and he knew it. IMO.
The use of her bank cards supports this as well. You don't leave someone you love without any money.