@mitu Hi, and thanks for your reply.
Apologies for having not provided feedback sooner, not normally my habit to be ill-mannered. I had to purchase a SATA to USB adapter so I could boot from my SSD with the pi removed from the case, then we had a family wedding ...
Anyway, you're absolutely right. With the case taken out of the equation, and the SN30 Pro connected directly to a USB port on the pi, ReDream launches fine. So, as you said, must be an issue with the USB port on the NESPi4 case.
As I say, I do have a different controller, also from 8BitDo, which doesn't experience the same issue. Possibly because that model has upgradeable firmware? So I'll most likely buy another one of those, one which colour matches the NESPi4.
Anyway, thanks again for the solution.