This is the EXACT failure I had with the KOOBOOK branded adapter.
Then lucky for you, I managed to salvage it! Maybe this method will also work for you, but it's Mac specific.
I used a USB SD card reader to mount the card in my MacBook Air (Ventura 13.4). The HFS+ OS8.1 partition was immediately mounted, which was pretty neat. That told me the problem was probably only a screwed-up driver partition on the SD card. I used Disk Utility to make a disk image of the OS8.1 partition, hoping this would save me from having to re-run the OS8.1 installer later. Then I reformatted the whole SD card as DOS MBR with FAT32 filesystem, intentionally choosing something that I hoped my 6300 would not recognize and try to mount.
Returning the SD card to my 6300, I no longer got chimes of death at startup. I re-ran Apple Disk Setup and it correctly detected the drive as 16 GB and formatted it with Apple File Partition. I then mounted the SD card on my MacBook Air a second time, as well as mounting the disk image I'd made earlier, and did a drag-and-drop copy of all the files from the image to the empty 16 GB partition.
Back on the 6300 again, this all worked as I'd hoped, except I had to drag the System file in and out of the System Folder to bless it.
This is super cool, I hadn't realized I could mount an old-school HFS+ parition from an SD card under the current version of OSX. That means it'll be very easy to get new software onto this 6300: just download it from the Garden, copy it to the OS8.1 partition on the SD card, and then stick the SD card back into the 6300.
It's actually easier than doing the comparable thing with a SCSI SD card emulator like Zulu SCSI or Blue SCSI, since as far as I know OSX and/or Disk Utility won't open the .hda files they use. You can still run them in a software emulator like Basilisk, but for simply moving files about that's not especially convenient.
As far as the SD adapter, I’d have to test mine in my 1400, but it feels pretty speedy. 1400 is pretty contemporary to the 6300.
Yes! I'm still getting 45 second boot times, which is a major improvement over the hard disk, even though HDT said the SD card was the same or worse performance as the hard disk. Maybe "sustained read speed" isn't the number I should be focusing on, and it's more about the access time? Maybe there isn't much performance difference between the two when reading a large file from contiguous sectors, but the SD card outperforms when doing lots of random reads with small transfer sizes? I'll need to play with the benchmark settings in HDT to see if I can find settings that are more representative of what happens during MacOS startup and typical Finder operations.