Mercurial's "histedit" command offers two operations to combine the commits: "fold" and "roll", where "fold" brings the earlier commit into the later commit and "roll" does the reverse. The "fold" operation does exactly what I want in this case: It brings all the changes into the final commit from when I actually finished it, using the commit date of that commit.
Git's "rebase -i" command offers "squash" and "fixup" and "fixup -c" and "fixup -C", but they all do the same thing as "roll", i.e. they keep the earliest commit's date, the date when I started working on the thing and not the date when I finished working on it. (So I then cut and paste the correct date and update the commit afterwards. This may not be the best way to do it.)