Hmmm... Sounds like a bit of a mess in there... Install disks aren't normally part of the Workbench disk set for some machines, so you're not necessarily missing them. It is fairly simple to set up the OS by hand, and all you'll need to do is modify your startup-sequence to get it to look in the correct places after you've copied everything from the floppies. Then it shouldn't ask for the floppies when you're booting.
If the drive's working fine after you boot from floppy, it does mean your controller and accelerator are getting on ok, and so once any special commands/libraries from the floppy are also on the HD there's no reason it shouldn't work the same way. Which leads me to suspect a filesystem mismatch somewhere. If you have a newer version of the filesystem on the boot floppy than you have in the ROM or the RDB, and it was formatted with the newer version, the older version will crash when it tries to mount the new version drive. As they can be stored in different places, you should find out what version is in each location. Can't remember the version that's in the 3.1 ROMs, but if any partitions are formatted with a newer version you'll have to have that version in the RDB as well. You can find the RDB version with HDToolbox and the one on the floppy by typing "version df0:L/fastfilesystem" in a shell window.
Could be way off the mark, but that's what this issue sounds like to me...
