[I also spent tons of time looking at the source code for both versions at the time, and both the similarities and differences were pretty clear.]
Without reviewing my Finseth, what is there besides buffer management and its linked redisplay, built in commands (a lot of which were copied, like my favorite marker of backup-by-copying-while-linked, which in the '80s was to my fairly extensive knowledge unique to Gosling EMACS), keymappings and the extension language? (Half my professional work in the '80s was on many different versions of EMACS, and I believe I worked on every significant UNIX one, although only Steve Zimmerman's CCA Emacs was a real competitor to Gosling/GNU EMACS as machines got enough memory. Note when I say "worked on" I might mean nothing more than porting; today's young whippersnappers are spoiled by the Linux mono-culture and/or modern package systems :-)
You say the first two "were tricky to get right" ... you've got that right, back in those days when resources were dear and performance was critical (Eight Megabytes And Constantly Swapping :-), they were in my opinion the hardest parts, especially since the superiority of the buffer gap vs. linked lines wasn't necessarily intuitive, and didn't the main file of the Gosling redisplay code have a skull and crossbones at the top? Although I'll admit to some bias since buffer management on the PDP-11 and non-VM PCs and 68000 workstations was problematic, in this case especially for a code base that started on a paging super-minicomputer (the VAX). Once you had those, building on top of them is fairly obvious, and a if not the largest part of the quality was a matter of taste, where RMS was vastly superior to Gosling, from using "standard" keymappings to a real LISP.
By the time this was playing out, I was intimately familiar with the C base of (UniPress) Gosling EMACS, from having finished a MS-DOS port and was working on an Amiga port. So it was no trouble to look at GNU EMACS to determine it was, in the the legal, copyright sense, a derivative work, not something that was influenced by it, which is not something that RMS/GNU were even claiming at the time.
They said, based on an email they claimed to have received (that as I recall they never produced, but as you note all this hardly matters), that they were authorized to start with an old version of Gosling EMACS, and they claimed they fixed this legally by rewriting every part of it they got from Gosling EMACS ... which doesn't cut it, legally. If UniPress had been run by junkyard dogs they could have done an USL v. BSDi and put the GNU under a legal cloud, except they probably would have won. It was an unconscionable risk for RMS to take.
Fortunately, all they did was verbally disagree, they thought GNU EMACS would create a bigger market for Gosling EMACS, which I'm sure was true for a while (the version GNU started with was ancient and missing a lot of polish), and that no one would win if they took it to the courts. It probably helped that they'd previously worked at Plauger's Whitesmiths and the separation was as ugly as you can imagine, although the legal drama was cut short when the other side's lawyer was caught burglarizing their office, which doesn't tend to impress judges....
Note the other comments in this discussion about how RMS isn't a good steward of many of the efforts under his control, and I'd add specifically "look at how GCC died and was replaced by a community version", the Lucid Emacs/XEmacs mess (in the link that points out RMS can't sing), and Hurd's beyond Duke Nukem Forever path.