Free File Sync can auto run when a sd.card is inserted. But you are probably going to want to give a unique folder name for each disk not sure how to do that.
I use a robocopy script to inject photos. Simply enter the drive letter and what you want the folder called.
I all likelihood having 6 SD cards reading at once is going to be slower overall than doing 3 batches of 2. USB kind of sucks that way.
Unless you are going to put 6 dedicated USB hosts in your PC.