I ended up putting System 7.1 and Update 3.0 on the machine which takes up only a few MB of space. Thanks for the recommendation!
Although this is probably the best option, I'm intending to stick with a traditional hard drive for authenticity/sentimental reasons. I might look into getting a more modern SCSI server drive or something like that, but for the purposes of this thread I wanted to know if there is some way I can rehab any of the failed drives with the resources I have on hand (i.e., an LC III with a working 40 MB HDD).