You could also transfer your roms via network (Batocera provides the 'share' partition via Samba, so it can be accessed no matter if you use Windows or something else), alternatively just download Ubuntu to an USB stick and boot from it. As it's Linux it will be able to display more than just 1 partition on your SD.
When using Linux you can also access the share partition via SSH / SFTP, too, so Linux definitely works best here.
By the way, PSP and Dreamcast emulation won't work very well on RPI3 as the hardware is not powerful enough for these systems (Odroid XU4 or an x86 based platform work better).