> Ultimately no code breaks, after all it is changing the associativity of an
> operator that is by definition *associative*. ;)

That's what I thought too, but I already gave an example:

a <> empty <+> b

This means different things depending on whether we use infixl or
infixr. And as I noted, this doesn't bite Text.PrettyPrint.Leijen
because it lacks the <+> unit law.

Bah. Good point.

So my tentative suggestion is:

infixr 6 <>
infixr 5 <+>
infixr 4 $$, $+$

So <> binds tighter than <+> and $$ and $+$ are still lower precedence
than <> and <+>, but switched round to being right associative.

Reasonable, but there is the caveat that causes another problem, which is that now <+>, : and ++ conflict, which was why we had to raise <> to 6 in the first place. We could adopt your proposed fix one level up though with:

infixr 7 <>

infixr 6 <+>

-Edward