I was reading a question, and I thought about an answer.
Then, I noticed that an answer was already posted to the question, which had the information that I was thinking about.
Then, I noticed that this answer was actually written by me, some time ago. However, few people would be able to see the answer, because it was deleted. Here is the URL I have (for whatever mods may be able to see it). https://superuser.com/a/861144/401839
I answer the key core question ("Does anybody know how I might be able to transfer the large files..."), and the question was deleted without explanation.
I decided to try to ask the question with minimal bother/footprint, by going to Root Access instead of posting to Meta. I asked about this. After a couple of minutes with no response, I backgrounded the tab in my browser. Thanks to YouTube, I got sufficiently sidetracked. Later, I mostly forgot about this and I think I closed a bunch of browser tabs rather rapidly, possibly including the Root Access chat. So, I opened a new tab to Root Access, and found that the comment I made (today about 6:15am PST?) was nowhere to be seen.
What was so terrible about this answer that a mod deleted it without explanation and even the chat room eliminates discussion about it?
The body of the answer, for non-10K users:
Glad you found a working solution.
ARJ is another option that supports creating archives across multiple archives. RAR probably can too. The nice thing about Arj is that there is an Open Source version of it.
Borland Turbo C++ had a text-mode full screen interface, and was a commercial project. Last version was 3.0 or 3.1, I forget which offhand. It was commercial. But then Borland C 3.x was released free. I think the free version didn't come with the nice full screen interface, though. 'twas just the compiler and other needed stuff, not the nicer interface.
Note that those old C(++) versions may not work with some more modern extensions that you may be used to.
What other drive letters do you have? What does your CONFIG.SYS load? I ask, because these may be clues about how to get a necessary device driver onto a bootable floppy so that you can access your compressed disk without needing to boot from the hard drive.
If you've got funds/patience and want to invest in this, consider getting an NE2K card. (a.k.a. NE2000, that's a fancy way of telling you to get an Ethernet card.) Of course, make sure it is compatible (ISA would most probably work). Otherwise, a modem might be a way to help get files off of the machine.