[This comment is about procedure names, not any deep issues.]

Regarding balanced/ (and its friends balanced-quotient and
balanced-remainder): Is the name "balanced" conventional/compelling
enough to use?

The main reason I ask is that one may argue that round/ (and friends)
are more balanced than balanced/ (and friends) in the sense that
balanced-remainder consistently favors -|d/2| over |d/2| while
round-remainder chooses between the two based on the sign of the
dividend.

Granted that balanced/ is more balanced than euclidean/ by this metric,
which may be the motivation for its name (and further that balanced/
makes no claims to being "most balanced").  Still, I found it a bit odd.

I'm hoping I have interpreted the operations correctly; this stuff seems
more confusing than it ought to be.

Regards,

-chaw