I ended up doing this in a roundabout fashion as I hadn't received the above suggestions in time.
I used the selection from the Feature Class to create a text file containing a list of the files I wanted called "PullFiles.txt"
I created a new folder called "HSO_WB_Files" and used PowerShell to copy the relevant files to that folder using the below script found online:
I batch imported all the CSV files into a GDB.
I then used a Model to Iterate through all the files and create XY point files from each
The suggestions by Bob and Dale are more elegant, but this worked anyway.