My other option, and the one I'd like to work with, is that I'd love to find a way to copy the contents of the ADF file into a directory on the hard drive of the Amiga and play it from there.
Well, you can only do this with games that actually use normal floppy filesystem for the game files. Many if not most floppy games used custom trackloader, and these can't be copied since there is no filesystem to copy from in the first place. Only very old (or modern) games can be copied (old ones being so old that trackloaders weren't yet developed, modern ones being hdd installable).
If you wish to copy the files off adf, there are several ways. One way is to write the adf to a disk, then copy off the disk. Another is to write the adf to RAD disk, then copy from RAD:, or use
XAD to copy from the adf directly:
xadunfile diskimage boingdemo.adf dest t: