Yes, if you had access to SATA, IDE, SCSI, and MFM/RLL controllers, BB Amiga would indeed be a very handy tool for accessing data on any old hard drives. With a Mac emulator added and a Mac floppy drive too if you wanted a "complete" solution.
The tricky part is assembling the software suite needed for such a purpose, but I think you've got most of that already by now.

If you do go that route, I daresay you will have an easy to use backup of the software suite, for completely resetting the system in between archive jobs.

It will save you an awful lot of work in the future.
For the moment, getting the data off of YOUR floppies and hard disk is the priority. After that, you can sit back and consider your next move.
I bet my decades old 3.5" Amiga PC disk are the same.
They should be in better condition than the 5.25 High Density disks. First, the magnetic layer on them is twice as thick. Second, they have a dust cover built in to keep out dust and smoke particles. Even a partial read of a disk is useful, somebody else might have an incomplete ADF, and between the two incomplete sets, a complete set of data can be reborn.