I am still looking around for a better solution but currently I am only using two crates since I only have two dogs, JRTs. Given the size of the Corgis, your crates are going to be a great deal smaller. I think you can fit three crates back there. Midwest does sell a product made for SUVs.
Here is a shot for an agility trial we competed at. My big boy JRT rescue, Scout is locked onto a dog competing in one of the two rings as the standard course was some 25' away. My other JRT, Chloe, isn't pictured as I am warming her up - Jacking her up and stretching her - before her run.
I can't do a solution right now because I plan to add two more dogs to the team.