Not sure I can answer your question specifically but I can tell you what I've always used for backups on Mac OS and have always been very happy with what it does. Retrospect backup software has been around since the mid 80's and at one point probably had the market share of Apple based backup products. It would certainly do what you're asking, but I'm not sure whether 1/ it backs up invisible files, I'd have to check one of my own manuals for it, and 2/ I'm not sure they did a version that would work on System 6.
However, knowing how good the software is, I wouldn't be at all surprised if it did backup invisible files and did have a version that worked on System 6.x. It is a commercial product and would therefore need to be purchased, probably through something like eBay if you can find the right version number. I certainly know that version 3.0 came out in the mid 90s so you'd probably need to be looking for versions 1.0 - 2.0 for compatibility with 6. I will check on version compatibility for version 3.0 though.
It's well worth doing some research into whether the early versions do work with System 6 because it's ideal for what you want to do. With luck someone here may know the answers to those two questions.
I don't know of any shareware programs that would do the same job.
I do have a copy of the backup utility that comes with the very early Apple Tape Backup 40SC and that certainly works on System 6, but I think that is machine specific and will only work with that Tape Drive.
However, knowing how good the software is, I wouldn't be at all surprised if it did backup invisible files and did have a version that worked on System 6.x. It is a commercial product and would therefore need to be purchased, probably through something like eBay if you can find the right version number. I certainly know that version 3.0 came out in the mid 90s so you'd probably need to be looking for versions 1.0 - 2.0 for compatibility with 6. I will check on version compatibility for version 3.0 though.
It's well worth doing some research into whether the early versions do work with System 6 because it's ideal for what you want to do. With luck someone here may know the answers to those two questions.
I don't know of any shareware programs that would do the same job.
I do have a copy of the backup utility that comes with the very early Apple Tape Backup 40SC and that certainly works on System 6, but I think that is machine specific and will only work with that Tape Drive.