Okay, after more searching, found out that the popular Disk Tools 1 and Disk Tools 2 do not work with anything earlier than a 68040, my Classic II being a 68030.
So, found, downloaded, and burned the disks for System 6 ... and my Macintosh spit it out without hesitation and booted to the HD.
Then, found, downloaded, and burned disks for System 7 ... Huzzah! Those worked wonderfully. Found out my HD has some damage that Disk Tools (the one that came with System 7) could not correct - so will eventually have to get a replacement HD.
For now, am initializing the HD. Will then attempt to install System 7 on the machine, then updated to 7.5.3, then 7.5.5.
Should be fun!