The copies extracted to floppy disks should behave as floppy disks.
If you mean edit an .adf so that correct file types are set (writable, editable, deletable) then you have to use something that can read the files as a usb stick / sd card with files on, like a regular PC running Windows or Linux).
Technically you could use an Amiga with a "real" usb port or sd card reader. (Which ever medium used by the floppy emulator).
PROTECT Usb0:Game.adf +rwd <- Assuming drive is mounted as Usb0: correctly and game file in root directory
Or an sd card attached in a compact flash adapter on PCMCIA:-
PROTECT CF0:Game.adf +rwd <- assumes CF0 has been mounted correctly, CF0 needs big sector size (4096) for cards 2GB-16GB, 8192 16-32GB cards
To mount the drive correctly (as a drive) you would also need Fat95 filesystem handler in your Amiga's L directory.
Is the hard drive one big partition and not even half full? That can cause some software to misread the free space available as negative (would generate "drive is full" message even though it isn't).
OK, there are replacement Workbench commands on 3.1.4 that work correctly (list, dir, info etc) but the game could be using it's own code which would have the same issue.
Filling up the partition with stuff so it's at least half full removes the problem on old Workbench software. Might work with the game trying to save to hard drive, might not.
EDIT: I'm assuming you are running your 4gb CF card as a hard drive and haven't upgradaed to something larger. There is some software that only likes running / operating on the first 4GB of any Amiga hard drive. For instance, PC Task and shapeshifter.